The value of c for which Rolle's theorem for the function $\mathrm{f}(x)=x^3-3 x^2+2 x$ in the interval $[0,2]$ are

A triangular park is enclosed on two sides by a fence and on the third side a straight river bank. The two sides having fence are of same length $x$. The maximum area (in sq. units) enclosed by the park is

A stone is dropped into a quiet lake and waves move in circles at speed of $8 \mathrm{~cm} / \mathrm{sec}$. At the instant when the radius of the circular wave is 12 cm . how fast is the enclosed area increasing?

If the half life of substance is 5 years, then the total amount of the substance left after 15 years, when initial amount is 64 gms is