Question

Evaluate the difference quotient for the given function. Simplify your answer. f(x) = 5 + 5x − x², f(5 + h) − f(5) divided by h

Answer 1

The difference quotient for the given function is -h - 5.

Explanation:

The difference quotient for the given function f(x) = 5 + 5x − x² is:

(f(5+h) - f(5)) / h

= ((5 + 5(5+h) - (5+h)²) - (5 + 5(5) - 5²)) / h

= ((25 + 5h - (h² + 10h + 25)) - (25)) / h

= (-h² - 5h) / h

= -h - 5