# How do you find the solutions for f'(3) f'(4) and f'(5), if you are given a graph with the curve #y=f(x)#?

##### 1 Answer

Jul 24, 2018

See details and example.

#### Explanation:

Make another graph for

f' values, respectively.

Exemplification:

g-graph:reveals values near 2.5, 3 and 3.5.

graph{(y - 1.5sqrtx)(x-3+0y)(x-4+0y)(x-5+0y)=0}.

4-sd values, by trial and error y-bracketing method:

Graph for 4-sd

graph{(y - 1.5 sqrt x)(x-3)=0[2.95 3.05 2.597 2.599]}

By substitution, f ' ( 4 ) = 3, exactly.

Graph for 4-sd

graph{(y - 1.5 sqrt x)(x-5)=0[4.95 5.05 3.353 3.355]}