# Calculus Examples

Find the second derivative.

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 second derivative of with respect to is .

Set the second derivative equal to then solve the equation .

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

No Inflection Points

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

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

The graph is concave down