If f(x)=a(x-cos\~x) is strictly decreasing in R, then 'a' belongs to

The relation between the height of the plant (y cm) with respect to exposure to sunlight is governed by the equation $y=4x-\frac{1}{2}x^{2}$, where x is the number of days exposed to sunlight. (i) Find the rate of growth of the plant with respect to sunlight. (ii) In how many days will the plant attain its maximum height? What is the maximum height?

Find the interval in which the function $f(x)=x^{4}-4x^{3}+10$ is strictly decreasing.

The area of the circle is increasing at a uniform rate of $2~cm^{2}/sec$. How fast is the circumference of the circle increasing when the radius $r=5$ cm?

Absolute minimum value of $f(x)=(x-2)^{2}+5$ in the interval [-3, 2] is :