Which of the following statements are true? (A) The function $f(x) = \frac{x^4}{4} - \frac{4}{3}x^3 + \frac{x^2}{2} + 6x$ has 3 critical points. (B) The function $f(x) = |x| + 3$ has no minimum value. (C) A local maximum value is always the absolute maximum value. (D) $f(x) = x^2$ has minima at $x=0$. Choose the **correct** answer from the options given below:

Consider the function $f(x) = \sin x$ in the interval $[\pi, 2\pi]$ then which of the following statements are correct?

(A) $x = \frac{3\pi}{2}$ is its stationary point.

(B) Its maximum value is 1

(C) Its minimum value is -1

(D) It attains its maximum value at $\pi$ and $2\pi$

Choose the correct answer from the options given below:

Match List-I with List-II

Choose the correct answer from the options given below:

If x is real, then minimum value of $x^2 - 8x + 17$ is :

If $f(x) = 2x^3 - 15x^2 + 36x + 1$, $x \in [1, 5]$, then the absolute minimum value of $f(x)$ is:

If the cost function of a product is given by $C(x) = \frac{3}{4}x^2 - 5x + 21$, then the marginal cost when $x = 10$ is

The angle of intersection between the curves $y = 4 - x^2$ and $y = x^2$ is :