Calculus 1 Derivatives question

Question

use the definition of the derivative to find the derivatives of the function

a)f(x) = x+1, a = 0

Answer 1

The derivative is defined as follows:

f'(x) = lim_h→0 f(x+h) - f(x) / h. In this case f(x+h) = (x+h)+1 = x+h+1.

Plugging in for f(x+h) and f(x) = x+1, we get:

f'(x) = lim_h→0 (x+h+1 - (x+1))/ h = lim_h→0(h/h) = lim_h→0 1 = 1.

This means that the derivative is always 1, so the answer is 1.