Let f(x) = −x2 + 6x. Find the difference quotient for f(4+h) - F(4)/h. (Simplify your answer completely.)

Question

Let f(x) = −x² + 6x.

Answer 1

f(x) = -x^2 +6x

f'(x)= -2x+6

f'(4) = -2(4)+6 = -2

f(4) = -16+24 = 8

f(4+h) = -(16+8h +h^2) +6(4+h) = -h^2 -2h +8

[f(4+h)-f(4)]/h = (-h^2-2h)/h = -h-2

= f'(4)=-2 when h=0

the difference quotient = the derivative

when h approaches zero