Calculus

When approaching a related rates question, follow these steps:

Read through the problem.

Draw a diagram

Write out three columns, entitled Given, Find, When.

Read through the problem again and fill out the columns appropriately.

Find the relating equation and find the derivative of both sides of the equation.

A function that is so complicated that an explicit rule for f(x) cannot be produced.

A normal exponential function:

Derivative:

OR

The derivative of an exponential function is proportional to the function itself.

The sign of the derivative of a function tells whether the original function is increasing or decreasing.

f' is negative = f is decreasing

f' is positive = f is increasing

f'' is negative = f' is decreasing, and f is concave down

A normal power function:

A constant function is a linear function that has a slope of 0.

The derivative of a constant function is also 0.

A normal constant function:

The slope of a linear line is a constant.

The derivative of a linear line is also a constant.

A normal linear function:

This can be used to find the derivative formula of a given function.