For the graph of function f given below,

Locate the point at which the graph falls the fastest when you move along the curve to the right.

The price of a share is given by the following equation.

$P\left(x\right)=3.7\sin \left(\frac{\pi }{113}\right(x-73\left)\right)+17$

Where x is the number of days after the share is launched.

Determine the period of P(x).

Demand function for an article is $D\left(p\right)=96-3p$ . Here D(p) is the number of article sold in a week when price of each article is $p.

If price is $6, how many articles is sold in a week?

The cost function C(x) and the selling price of each article, p(x) are given below. Determine the profit function P(x).

$C\left(x\right)=-0.03x^2+70x+75$

$p\left(x\right)=80$

A balloon is being filled with air, and its volume $V$ after $t$ minutes is given by $V=4t^2$, where $V$ is measured in liters. Draw the graph of the function and the secant line passing through $A$ and $B$. The endpoints of the interval $1\leq{t}\leq{3}$ correspond to $A$ and $B$. Then, calculate the slope of the secant line and interpret it in terms of an average rate of change over the interval.