$f(x)=\sin x+\frac{1}{2} \cos 2 x \text { in }\left[0, \frac{\pi}{2}\right]$ (A) $f^{\prime}(x)=\cos x-\sin 2 x$ (B) The critical points of the function are $x=\frac{\pi}{6}$ and $x=\frac{\pi}{2}$ (C) The minimum value of the function is $2$ (D) The maximum value of the function is $\frac{3}{4}$ Choose the correct answer from the options given below :

The function $f(x) = \frac{-3}{4}x^4 - 8x^3 - \frac{45}{2}x^2 + 163$ has a local maxima at

The function $f(x) = 4 - 3x + 3x^2 - x^3$ is (Here $\mathbb{R}$ is set of real numbers)

The function $f(x) = tanx - x$

The volume of a cube is increasing at the rate 9 $cm^3/s$. How fast is the surface area increasing when the length of an edge is 10 cm ?

The absolute maximum value of the function $f(x) = 2x^3 - 15x^2 + 36x + 7$ on the interval [1,5] is

The rate of change of the area of a circle with respect to its radius $r$, when $r = 3$cm, is: