How do you solve this problem?

Question

Finding the derivative at an unspecified point

use this formula to solve the problem : f '(x)= lim f(x+h)-f(x)/h
h->0
problem : f(x)=x^2+3x-7

please show the steps

Answer 1

f(x) = x² + 3x - 7

f(x + h) = (x + h)² + 3(x + h) - 7

f(x + h) = x² + h² + 2xh + 3x + 3h - 7

f(x + h) - f(x) = [x² + h² + 2xh + 3x + 3h - 7] - [x² + 3x - 7]

f(x + h) - f(x) = x² + h² + 2xh + 3x + 3h - 7 - x² - 3x + 7

f(x + h) - f(x) = h² + 2xh + 3h

Take out common term h.

f(x + h) - f(x) = h(h + 2x + 3)

Fundamental theorem of differentiation formula:

But f(x + h) - f(x) = h(h + 2x + 3)