Question

Use the definition of derivative to find the derivative of f(x) = 3x + 2. Show your work.

Answer 1

derivative of 3x + 2 = derivative of 3x + derivative of 2
do you know how to find each of them?

Answer 2

what is the derivative of 3x? and what is the dervative of 2(or any constant)?

Answer 3

3 and 0

Answer 4

whats 3 + 0?

Answer 5

there u go o: 3 + 0

Answer 6

3

Answer 7

ok the problem here is that it says use the deffinition, so
lim h->0 of (f(x+h)-f(x))/h

Answer 8

so lim h->0 (3(x+h)+2-(3x+2))/h

Answer 9

\[f'(x)=\lim_{h \rightarrow o} \frac{f(x+h)-f(x)}{h}\]

f(x+h)=3(x+h)+2
f(x+h)-f(x)=3x+3h+2-3x-2
=3h

\[f'(x)=\lim_{h \rightarrow o} \frac{f(x+h)-f(x)}{h}\]
=\[\lim_{h \rightarrow 0}\frac{3h}{h}\]
=
\[\lim_{h \rightarrow 0}3=3\]

Answer 10

= lim h->0 (3x+3h+2-3x-2)/h

Answer 11

you can do the rest right?

Answer 12

sorry but i am very lost

Answer 13

i know how to find the derivative, but i am confused on how to use the definition to explain it

Answer 14

do you see that first function that @THE_PROPHET wrote?

Answer 15

yes

Answer 16

that is the deffinition of the derivative of a function

Answer 17

ok

Answer 18

so since your f(x) = 3x+2
(f(x+h)-f(x))/h = (3(x+h)+2 - (3x+2))/h
= (3x+3h+2-3x-2)/h
= 3h/h = 3

Answer 19

perfect, thank you so much!!!!