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?

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?

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

A differentiable function $f(x)$ has a local maximum at $x = 0$. Let $y = 2f(x) + ax - b$.

Which of the following is/are correct?

1. $f'(0) = 0$

2. $f''(0) < 0$

Select the correct answer using the code given below: