Differentiable function problem

Question

A differentiable function f(x) has derivative at x = 3 equal to 7. Approximate the change in the function that occurs as x changes from x = 3 to x = 3.01

Answer 1

The tangent line is the best linear approximation to f. We're told ƒ^'(3) = 7. (In case it's hard to read- it looks funny on my screen- that's "f prime of 3"). That's the slope of the tangent line. f

(3.01) - f(3) ≈ ƒ^'(3) * (3.01 - 3) = 7 * 0.01 = 0.07