Question

Find the derivative of f(x) = 3x + 8 at x = 4.

Answer 1

using short cuts
f'(x) = 3
therefor, f'(4) = 3.

using the definition of a derivative
\[f'(x) = (f(x + h) - f(x))/(h)\]
\[f(x) = 3x + 8\]
\[f(x+h) = 3(x + h) + 8\]
\[f(x+h) = 3x + 3h + 8\]
\[f(x+h)-f(x) = 3x + 3h + 8 - 3x - 8\]
\[f(x+h)-f(x) = 3h\]
\[f'(x) = 3h/h\]
\[f'(x) = 3\]