Question

Please help, I am completely lost. the explanation in the lesson didn't do anything for me.
Find the derivative of f(x) = 4x + 7 at x = 5.

Answer 1

derivative(f(x))=(f(x+h)-f(x))/h as h tends to 0

Answer 2

in this case, the derivative is (f(5+h)-f(5))/h as h tends to zero.

Answer 3

i am not really sure what to do with this info tbh :(

Answer 4

plug in for f. what is f(5+h)? what is f(5)?

Answer 5

in this case, since the derivative is the slope of the tangent line at a given x value, f'(x)=5.

Answer 6

you can verify this by calculating it manually.
f(5+h)=4*(5+h)+7
f(5)=4*5+7

Answer 7

f(5)=27

Answer 8

but what do i do after that?

Answer 9

calculate f(5+h). subtract f(5) from f(5+h).

Answer 10

okay give me a moment

Answer 11

so i solve for h?

Answer 12

nope. just calculate f(5+h)-f(5) in terms of h.

Answer 13

i feel retarded right now...

Answer 14

would you mind working out the problem set by step so that I can use it as reference or link me to a good video on the subject because i have no idea what im doing

Answer 15

sure.
f'(x)=limit of (f(x+h)-f(x))/h, as h->0
f'(5)=(f(5+h)-f(5))/h
f(5+h)=4*(5+h)+7=4h+27
f(5)=4*5+7=27
f(5+h)-f(5)=(4h+27)-(27)=4h
(f(5+h)-f(5))/h=4h/h=4.
Thus the derivative is 4.

Answer 16

have you studied limits yet?

Answer 17

i read the lesson in the textbook but i didnt really absorb anything from it

Answer 18

i get the concepts though

Answer 19

i just dont really work well without a teacher

Answer 20

i dont really understand what happens between the last two lines of your explanation
f(5+h)-f(5)=(4h+27)-(27)=4h
(f(5+h)-f(5))/h=4h/h=4

Answer 21

i understand the first line but as soon as i see the next line it is a mystery to me

Answer 22

which part is unclear, (f(5+h)-f(5))=4h, (f(5+h)-f(5))/h=4h/h, or 4h/h=4?

Answer 23

i think something just clicked in my brain

Answer 24

can i do one and you check it for me?

Answer 25

sure :)

Answer 26

something came up IRL so i will be back in around 20 minutes if that is okay with you

Answer 27

Thank you for your help even if you cant wait for me.