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:

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

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

The function $y$ has a relative maxima at $x = 0$ for

Let $f(x)=|x-1|, g(x)=[x]$ and $h(x)=f(x) g(x)$ where [.] is greatest integer function.

What is $\int\limits_{-1}^{0} h(x) dx$ equal to?

Let $f(x)=|x-1|, g(x)=[x]$ and $h(x)=f(x) g(x)$ where [.] is greatest integer function.

What is $\int_{0}^{2} h(x) dx$ equal to?