Find an expression for derivative of the following function.

$g\left(x\right)=\frac{-4x}{x^2+1}$

Find an expression for derivative of the following function.

$h\left(x\right)=(x+2)(x-7)$

Find an expression for derivative of the following function.

$i\left(x\right)=(2x+3{)}^3$

Which of the following graph satisfies the following condition?

$\underset{x\to \infty }{\lim }f\left(x\right)=2$

Which of the following graph satisfies the following condition.

The derivative of $f$ is always negative.

A particle $P$ moves in a straight line. Its position, $s$, after $t$ seconds is described by the following graph.

State the intervals in which the particle is moving away from the origin.

A particle $P$ moves in a straight line. Its position, $s$, after $t$ seconds is described by the following graph.

State the intervals in which the particle is at rest.