The interval in which the function $f(x) = 2x^3 - 3x^2 - 36x + 7$ is strictly decreasing is :

For the function $f(x)=x^4-2x^2+5, x\in R$, then which of the following statements are True?

A. $f(x)$ is increasing on $(-\infty,-1)$

B. $f(x)$ is decreasing on $(-\infty,-1)$

C. $f(x)$ is increasing on $(-1,0)\cup(1,\infty)$

D. $f(x)$ is decreasing on $(1,\infty)$

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Match List-I with List-II

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For the function $f(x)=2x^3-9x^2+12x-5, x \in [0,3]$, which of the following statements are correct ?

A. The point of absolute maxima is x=3.

B. The absolute minimum value is -1.

C. The critical points are x=1 and x=2.

D. The absolute maximum value is 3.

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If $x = -1$ and $x = -2$ are the extreme points of $f(x) = \alpha\log|x| + \beta x^2 + x$ then

If the interval in which the function $f(x) = 4x^3 - 6x^2 - 72x + 30$ is strictly decreasing, is (a,b) then a+b is equal to

For which of the following real functions, $x=0$ is a point of local maxima?

(A) $f(x)=4x^4-3x^3-2x^2+1$

(B) $f(x)=3x^5+\sqrt{2}x^4-7x^2+4$

(C) $f(x)=5x^4-3x^2+e$

(D) $f(x)=-3x^3+2x^2-9$

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