Derivatives of Quadratic Polynomials
View the Lesson | MATHguide homepage Updated June 22nd, 2023


Status: Waiting for your responses.

Given:f(x) = 2x2 + 10x + 8
Problem:Determine the derivative of f(x) using the definition of a derivative.

f ' (x) = lim
f(x+h) - f(x)
h
h→0

f ' (x) = lim
2(x+h)2+(x+h)+8 - (2x2+10x+8)
h
h→0

f ' (x) = lim
2(x2+xh+h2)+10(x+h)+8 - (2x2+10x+8)
h
h→0

f ' (x) = lim
2x2+xh+2h2+10x+10h+8 + x2-10x-8
h
h→0

f ' (x) = lim
xh+h2+h
h
h→0

f ' (x) = lim
h(x+h+)
h
h→0

f ' (x) = limx+h+
h→0

f ' (x) =  x+