Question

Using the definition of derivative, and find f'(x). Then find f'(-2), f'(0), and f'(3) when the derivative exists.

Answer 1

What is \(f(x)\)?

Answer 2

its number 11 from the attachment

Answer 3

f(x)=3x-7

Answer 4

\[f'(x)=\lim_{h\to0}\frac{\bigg(3(x+h)-7\bigg)-\bigg(3x-7\bigg)}{h}\]
\[f'(x)=\lim_{h\to0}\frac{3x+3h-7-3x+7}{h}\]
\[f'(x)=\lim_{h\to0}\frac{3h}{h}\]
\(\vdots\)

Answer 5

\[f \prime \left( x \right)=\lim_{h \rightarrow 0}\frac{ f \left( x+h \right)-f \left( x \right) }{ h }\]

Answer 6

and what do i do with the f'(-2), f'(0),f'(3)??

Answer 7

Do i plug it in for x

Answer 8

as calculated above f'(x)=3
now you can find ?

Answer 9

so i do plug it in?

Answer 10

whatever you plug in the value will come out to be 3.

Answer 11

can you do me the first problem so i can see visually and understand it because im lost

Answer 12

f'(x)=3
f'(-2)=3
f(0)=3
..........

Answer 13

how?

Answer 14

there is no x in f'(x)
hence it will remain 3