Question

Evaluate the difference quotient for the given function. Simplify your answer.
f(x) = 3 + 3x − x2,
f((5 + h) − f(5))/h

Answer 1

$f(x)=3+3x-x^2;\ x_0=5\\\\\dfrac{f(x_0+h)-f(x_0)}{h}=\dfrac{3+3(5+h)-(5+h)^2-(3+3\cdot5-5^2)}{h}\\\\=\dfrac{3+15+3h-(25+10h+h^2)-(3+15-25)}{h}\\\\=\dfrac{18+3h-25-10h-h^2-(-7)}{h}\\\\=\dfrac{-h^2-7h-7+7}{h}\\\\=\dfrac{-h^2-7h}{h}\\\\=\boxed{-h-7}$