The maximum or minimum of a quadratic function occurs at . If is negative, the maximum value of the function is . If is positive, the minimum value of the function is .

occurs at

Find the value of equal to .

Substitute in the values of and .

Remove the parentheses from the numerator.

Remove the parentheses from the denominator.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Multiply .

Multiply by .

Multiply by .

Replace the variable with in the expression.

Simplify each term.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Apply the product rule to .

Raise to the power of .

Raise to the power of .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Subtract from .

The final answer is .

Use the and values to find where the maximum occurs.

Find the Maximum/Minimum Value h(t)=72t-16t^2