Direction : Consider the following for the items that follow :

Let f(x) = cos2x + x on [-π/2, π/2]. 

Direction : Consider the following for the items that follow :

Let f(x) = cos2x + x on [-π/2, π/2]. 

The non-negative values of $b$ for which the function $\frac{16x^3}{3} - 4bx^2 + x$ has neither maximum nor minimum in the range $x>0$ is

Consider the following for the next two (02) items that follow:

Let $\varphi(a) = \int_{a}^{a + 100 \pi} |\sin x| dx$

What is $\varphi(a)$ equal to?