The maximum value of the function $f(x)=\sin x(1+\cos x)$ in the internal $[0,\pi]$ is

The function $f(x) = x^2 - x + 1$ is

The cost function of a product is given by $C(x)=\frac{1}{3}x^3-45x^2-900x+36$, where x is the number of units produced. In order to minimize the marginal cost, how many units of the product must be produced?

The sides of an equilateral triangle are increasing at the rate of 5 cm/sec. The rate at which the area increases when the side is 20 cm, is

The interval in which $f(x)=-2x^3-9x^2-12x+1$ is increasing, is:

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 $(2, 3)$.

A square board of side 36cm is made into a box without top by cutting a square from each corner and folding up the flaps to form a box then maximum volume of the box is