# Calculus Examples

Find the first derivative.

By the Sum Rule, the derivative of with respect to is .

Evaluate .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Multiply by .

Evaluate .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Multiply by .

Since is constant with respect to , the derivative of with respect to is .

Add and .

Find the second derivative.

By the Sum Rule, the derivative of with respect to is .

Evaluate .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Multiply by .

Since is constant with respect to , the derivative of with respect to is .

Add and .

The derivative of with respect to is .

Rewrite the equation as .

Since , there are no solutions.

No solution

No solution

No values found that can make the second derivative equal to .

No Inflection Points

There are no inflection points and the interval to test the concavity on is .

The graph is concave down because the second derivative is negative.

The graph is concave down