Tìm m để đồ thị 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-mn MJXp-script" id="MJXp-Span-7" style="vertical-align: 0.5em;">3</span></span><span class="MJXp-mo" id="MJXp-Span-8" style="margin-left: 0.267em; margin-right: 0.267em;">−</span><span class="MJXp-mo" id="MJXp-Span-9" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-10">m</span><span class="MJXp-mo" id="MJXp-Span-11" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mn" id="MJXp-Span-12">2</span><span class="MJXp-mo" id="MJXp-Span-13" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-msubsup" id="MJXp-Span-14"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-15" style="margin-right: 0.05em;">x</span><span class="MJXp-mn MJXp-script" id="MJXp-Span-16" style="vertical-align: 0.5em;">2</span></span><span class="MJXp-mo" id="MJXp-Span-17" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mo" id="MJXp-Span-18" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-19">m</span><span class="MJXp-mo" id="MJXp-Span-20" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mn" id="MJXp-Span-21">5</span><span class="MJXp-mo" id="MJXp-Span-22" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-23">x</span><span class="MJXp-mo" id="MJXp-Span-24" style="margin-left: 0.267em; margin-right: 0.267em;">−</span><span class="MJXp-mn" id="MJXp-Span-25">4</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-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">3</span></span></span></span><span id="MJXc-Node-10" 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-11" 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-12" 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-13" 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-14" 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-15" 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-16" class="mjx-msubsup"><span class="mjx-base"><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;">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-18" class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">2</span></span></span></span><span id="MJXc-Node-19" 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-20" 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-21" 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-22" 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-23" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">5</span></span><span id="MJXc-Node-24" 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-25" 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-26" 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-27" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">4</span></span></span></span></span></span></span><script type="math/tex" id="MathJax-Element-1">\large y=x^3-(m+2)x^2+(m+5)x-4</script> có hai điểm cự

Tìm m để đồ thị hàm số y=x3(m+2)x2+(m+5)x4y=x3(m+2)x2+(m+5)x4 có hai điểm cự

4.8/5

Tác giả: Thầy Tùng

Đăng ngày: 18 Aug 2022

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Câu hỏi:

Tìm m để đồ thị hàm số y=x3(m+2)x2+(m+5)x4y=x3(m+2)x2+(m+5)x4 có hai điểm cực trị nằm khác phía với trục hoành.

Đáp án án đúng là: A

Lời giải chi tiết:

Tập xác định: D=R

Ta có phương trình hoành độ giao điểm của đồ thị hàm số và trục Ox là:

x3(m+2)x2+(m+5)x4=0(1)(x1)[x2(m+1)x+4]=0

[x=1x2(m+1)x+4=0(2)

Đồ thị hàm số có hai điểm cực trị nằm khác phía với trục hoành  phương trình (1) có 3 nghiệm phân biệt  phương trình (2) có 2 nghiệm phân biệt x1;x21

{Δ(2)=m2+2m15>01m1+40 {m4[m>3m<5

Vậy chọn phương án A.