If the function $f(x) = x^4 - 62x^2 + ax + 9$ has a critical point at $x = 1$, then $a$ is equal to:

A solid sphere of gold of radius 5 cm, is being melted in a furnace such that the radius is decreasing uniformly. When the radius is 1cm, the rate at which surface area (A) is decreasing w.r.t. time ($t$) is equal to

($\frac{dv}{dt}$ = rate at which volume is decreasing w.r.t. $t$)

For x ∈ ℝ - {0}, the function f(x) = $\frac{3}{x}$ + 7 is decreasing when

The edge of a cube is increasing at a rate of 7 cm/s. The rate of change of area of the cube when its side is 3 cm is:

A function $f(x)=\sin x(1+\cos x), x \in [0,\pi]$ has a local maxima at $x=$

For the function $f(x) = e^x + e^{-x}$

(A) $f'(x) = e^x - e^{-x}$

(B) The critical point is $x = 0$

(C) The minimum value is 1

(D) $x = 0$ is the point of local minimum.

Choose the correct answer from the options given below:

The slope of normal to the curve $y = 3x^2 + 3 \sin 3x$, at $x = 0$ is: