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-mstyle" id="MJXp-Span-5"><span class="MJXp-mfrac" id="MJXp-Span-6" style="vertical-align: 0.25em;"><span class="MJXp-box"><span class="MJXp-mn" id="MJXp-Span-7">1</span></span><span class="MJXp-box" style="margin-top: -0.9em;"><span class="MJXp-denom"><span><span class="MJXp-rule" style="height: 1em; border-top: none; border-bottom: 1px solid; margin: 0.1em 0px;"></span></span><span><span class="MJXp-box"><span class="MJXp-mn" id="MJXp-Span-8">3</span></span></span></span></span></span></span><span class="MJXp-msubsup" id="MJXp-Span-9"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-10" style="margin-right: 0.05em;">x</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-11" style="vertical-align: 0.5em;"><span class="MJXp-mn" id="MJXp-Span-12">3</span></span></span><span class="MJXp-mo" id="MJXp-Span-13" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mo" id="MJXp-Span-14" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-15">m</span><span class="MJXp-mo" id="MJXp-Span-16" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mn" id="MJXp-Span-17">1</span><span class="MJXp-mo" id="MJXp-Span-18" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-msubsup" id="MJXp-Span-19"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-20" style="margin-right: 0.05em;">x</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-21" style="vertical-align: 0.5em;"><span class="MJXp-mn" id="MJXp-Span-22">2</span></span></span><span class="MJXp-mo" id="MJXp-Span-23" style="margin-left: 0.267em; margin-right: 0.267em;">−</span><span class="MJXp-mo" id="MJXp-Span-24" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-25">m</span><span class="MJXp-mo" id="MJXp-Span-26" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mn" id="MJXp-Span-27">1</span><span class="MJXp-mo" id="MJXp-Span-28" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-29">x</span><span class="MJXp-mo" id="MJXp-Span-30" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mn" id="MJXp-Span-31">1</span></span></span></span><script type="math/tex" id="MathJax-Element-1">\large y=\dfrac{1}{3} x^{3}+(m+1) x^{2}-(m+1) x+1</script> đồng biến t

Hàm số y=13x3+(m+1)x2(m+1)x+1 đồng biến t

4.6/5

Tác giả: Thầy Tùng

Đăng ngày: 18 Aug 2022

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Câu hỏi:

Hàm số y=13x3+(m+1)x2(m+1)x+1 đồng biến trên tập xác định của nó khi:

Đáp án án đúng là: A

Lời giải chi tiết:

y=x2+2(m+1)xm1

Để hàm số đã cho đồng biến trên R khi và chỉ khi:

y=f(x)=x2+2(m+1)xm10xRΔ=(1m+m+1=m2+3m+202m1