Question

use the given graph to estimate the value of each derivative.
(a) f(0)
(b) f(1)
(c) f(2)
(d) f(3)
(e) f(4)
(f) f(5)

Explanation:

Step1: Recall derivative is slope

The derivative $f'(x)$ is the slope of the tangent - line to $y = f(x)$ at $x$.

Step2: Estimate slopes at points

Estimate the slope of the tangent - line at $x = 0,1,2,3,4,5$ from the graph.

Answer:

(a) $f'(0)\approx1$
(b) $f'(1)\approx0$
(c) $f'(2)\approx - 1$
(d) $f'(3)\approx - 1$
(e) $f'(4)\approx0$
(f) $f'(5)\approx1$