Question

$( 2x + 3 ) ( 4 - 3x )^{3} ( x-4 ) / ( x-2 )^2 x ^5\leq 0$

Answer 1

Answer:

ANSWER

The function f′(x) is given by

$${f}'(x)=\begin{cases}\brSpace 3x^{2}+2x-10 & \text -1\leq x< 0 \\ \brSpace \cos x & \text 0\leq x<\pi /2 \\ \brSpace -\sin x & \text  \pi /2 \leq x\leq \pi  \brSpace \end{cases}$$ 

The function f(x) is not differentiable at x=0, x=π/2

 as f′(0−)=−10, f′(0+)=1; f′(π/2−)=0, f′(π/2+)=−1.

The critical points of f are given by f′(x)=0 or x=0, π/2.

Since f′(x)<0 for −1≤x≤0 and f′(x)>0 for 0≤x<π/2

Therefore, f(x) has local maximum at x=0

Also f′(x)>0 for 0≤x<π/2 and f′(x)<0 for π/2≤x≤π

Therefore, f(x) has local minimum at x=π/2

Ans: A,C

Step-by-step explanation:

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