Cho hàm số <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-1"><span class="MJXp-mstyle" id="MJXp-Span-2"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-3">y</span><span class="MJXp-mo" id="MJXp-Span-4" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-msubsup" id="MJXp-Span-5"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-6" style="margin-right: 0.05em;">x</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-7" style="vertical-align: 0.5em;"><span class="MJXp-mn" id="MJXp-Span-8">3</span></span></span><span class="MJXp-mo" id="MJXp-Span-9" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mo" id="MJXp-Span-10" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mn" id="MJXp-Span-11">1</span><span class="MJXp-mo" id="MJXp-Span-12" style="margin-left: 0.267em; margin-right: 0.267em;">−</span><span class="MJXp-mn" id="MJXp-Span-13">2</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-14">m</span><span class="MJXp-mo" id="MJXp-Span-15" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-msubsup" id="MJXp-Span-16"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-17" style="margin-right: 0.05em;">x</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-18" style="vertical-align: 0.5em;"><span class="MJXp-mn" id="MJXp-Span-19">2</span></span></span><span class="MJXp-mo" id="MJXp-Span-20" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mo" id="MJXp-Span-21" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mn" id="MJXp-Span-22">2</span><span class="MJXp-mo" id="MJXp-Span-23" style="margin-left: 0.267em; margin-right: 0.267em;">−</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-24">m</span><span class="MJXp-mo" id="MJXp-Span-25" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-26">x</span><span class="MJXp-mo" id="MJXp-Span-27" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-28">m</span><span class="MJXp-mo" id="MJXp-Span-29" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mn" id="MJXp-Span-30">2</span><span class="MJXp-mo" id="MJXp-Span-31" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mn" id="MJXp-Span-32">1</span><span class="MJXp-mo" id="MJXp-Span-33" style="margin-left: 0em; margin-right: 0em;">)</span></span></span></span><span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML MJXc-processed" tabindex="0" style="font-size: 127%;"><span id="MJXc-Node-1" class="mjx-math"><span id="MJXc-Node-2" class="mjx-mrow"><span id="MJXc-Node-3" class="mjx-mstyle"><span id="MJXc-Node-4" class="mjx-mrow" style="font-size: 120%;"><span id="MJXc-Node-5" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.199em; padding-bottom: 0.495em; padding-right: 0.006em;">y</span></span><span id="MJXc-Node-6" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.101em; padding-bottom: 0.298em;">=</span></span><span id="MJXc-Node-7" class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span id="MJXc-Node-8" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.199em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span id="MJXc-Node-9" class="mjx-texatom" style=""><span id="MJXc-Node-10" class="mjx-mrow"><span id="MJXc-Node-11" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">3</span></span></span></span></span></span><span id="MJXc-Node-12" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.445em;">+</span></span><span id="MJXc-Node-13" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.445em; padding-bottom: 0.593em;">(</span></span><span id="MJXc-Node-14" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">1</span></span><span id="MJXc-Node-15" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.445em;">−</span></span><span id="MJXc-Node-16" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">2</span></span><span id="MJXc-Node-17" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.199em; padding-bottom: 0.298em;">m</span></span><span id="MJXc-Node-18" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.445em; padding-bottom: 0.593em;">)</span></span><span id="MJXc-Node-19" class="mjx-msubsup"><span class="mjx-base"><span id="MJXc-Node-20" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.199em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span id="MJXc-Node-21" class="mjx-texatom" style=""><span id="MJXc-Node-22" class="mjx-mrow"><span id="MJXc-Node-23" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">2</span></span></span></span></span></span><span id="MJXc-Node-24" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.445em;">+</span></span><span id="MJXc-Node-25" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.445em; padding-bottom: 0.593em;">(</span></span><span id="MJXc-Node-26" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">2</span></span><span id="MJXc-Node-27" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.445em;">−</span></span><span id="MJXc-Node-28" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.199em; padding-bottom: 0.298em;">m</span></span><span id="MJXc-Node-29" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.445em; padding-bottom: 0.593em;">)</span></span><span id="MJXc-Node-30" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.199em; padding-bottom: 0.298em;">x</span></span><span id="MJXc-Node-31" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.445em;">+</span></span><span id="MJXc-Node-32" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.199em; padding-bottom: 0.298em;">m</span></span><span id="MJXc-Node-33" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.445em;">+</span></span><span id="MJXc-Node-34" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">2</span></span><span id="MJXc-Node-35" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.445em; padding-bottom: 0.593em;">(</span></span><span id="MJXc-Node-36" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">1</span></span><span id="MJXc-Node-37" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.445em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></span><script type="math/tex" id="MathJax-Element-1">\large y=x^{3}+(1-2 m) x^{2}+(2-m) x+m+2(1)</script>. Tìm tập hợp

Cho hàm số y=x3+(12m)x2+(2m)x+m+2(1)y=x3+(12m)x2+(2m)x+m+2(1). Tìm tập hợp

4.6/5

Tác giả: Thầy Tùng

Đăng ngày: 18 Aug 2022

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Câu hỏi:

Cho hàm số y=x3+(12m)x2+(2m)x+m+2(1)y=x3+(12m)x2+(2m)x+m+2(1). Tìm tập hợp tất cả các giá trị thực của m để đồ thị hàm số (1) có điểm cực đại, điểm cực tiểu, đồng thời hoành độ của điểm cực tiểu nhỏ hơn 1.

Đáp án án đúng là: B

Lời giải chi tiết:

Chọn B

Cho hàm số y=3x2+2(12m)x+(2m). Δ=(12m)23(2m)=4m2m5

Hàm số có hai cực trị Δ>04m2m5>0m(;1)(54;+)(1) 

Theo đề bài hoành độ cực tiểu là x=2m1+4m2m53<1 4m2m5<42m

{42m>04m2m504m2m5<(42m)2 {m<2m(;1][54;+)m<75 m(;1][54;75)(2)

Từ (1), (2) suy ra m(;1)(54;75) thỏa ycbt.