The interval in which the function, $f(x) = 7 - 4x - x^2$ is strictly increasing is

For the function $f(x) = |\sin 4x + 3|$, then which of the following statements are correct ?

A. Minimum value of $f(x)$ is 2

B. There is no minimum value

C. Maximum value of $f(x)$ is 4

D. Maximum value of $f(x)$ is 3

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Function $f(x) = x + \frac{1}{x}, x \neq 0$ is increasing in the interval

Match List-I with List-II

Consider the function f(x) = 2x³ - 21x² + 36x + 80, x∈[0, 6]. Then

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For the function $f(x) = (x+1)^2(x-2)^2$, which of the following statements are TRUE?

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

(B) $f(x)$ is increasing on $\left(-1,\frac{1}{2}\right)$

(C) $f(x)$ is decreasing on $\left(\frac{1}{2},2\right)$

(D) $f(x)$ is increasing on $(2,\infty)$

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If $f(x) = (x+3)e^{-x}$, then which of the following statements are True?

(A) Function $f(x)$ is increasing on $(-2, \infty)$.

(B) Function $f(x)$ is decreasing on $(-2, \infty)$.

(C) Function $f(x)$ is increasing on $(-\infty, -2)$.

(D) Function $f(x)$ is decreasing on $(2, 3)$.

Which of the following functions has a local minima at $x = 0$?

(A) $f(x) = x^3$

(B) $f(x) = |x|$

(C) $f(x) = x^2$

(D) $f(x) = x^{-2}$

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