The function $y=x^{4}-6x^{2}+8x+11$ ha

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:

The function $y=x^{4}-6x^{2}+8x+11$ has a minimum at $x$ equal to

Options:

$1$

$-2$

$3$

$4$

Correct Answer:

$-2$

Explanation:

$\begin{aligned}f^{\prime}(x)&=0\\ 4x^{3}-12x+8&=0\\ x&=-2,1\\ f^{\prime \prime}(x)&=12x^{2}-12\\ f^{\prime \prime}(-2)&=36>0\end{aligned}$