Question

(1 pt) Suppose that f'(x) = 5 x for all x. Compute f(2) if:


f(10) = 0
f(2) =

f(-8) = 10
f(2) =

Answer 1

This is probably ridiculously simple but I'm sleepy and I think I'm missing something... Hahaha

Answer 2

Do you know integration?

Answer 3

I actually don't think we've covered integration no, is there another way to do this? Or if integration is a short topic to learn maybe it's hidden in my notes somewhere.

Answer 4

antiderivative is another name for it

Answer 5

what is a function that has a derivative of 5x?

Answer 6

f'(x) - (f(b)-f(a)/b-a) is this a formula to find this answer? Hahaha

Answer 7

i dont think so, tht looks like the mean value thrm

Answer 8

derivatives are a basic process that finds one function from another.

if we are given a function, f(x), we can determine its derivative f'(x) real simple by following a few simple rules.

when we want to work this in reverse, its tricky but not as tricky as youd think ... we simply have to undo the rules

Answer 9

Yeah that's MVT. I'm not seeing this in my notes, I did miss one class so it was probably covered then.

Answer 10

spose i asked you to find the derivative of kx^2 what would you try to do?

Answer 11

x^2+k*2x

Answer 12

well, assuming you just tried a product rule: k is an arbitrary constant and the derivative of a constant is 0 so

0x^2 + 2kx = 2k x

Answer 13

Oh yeah my fault. I know derivatives just sleepy lol

Answer 14

now, we have 5x given as the derivative so we know it has to come from some kx^2 function right?

Answer 15

2kx = 5x when k=?

Answer 16

2.5

Answer 17

5/2 yes :) now, here is the trickiness of it all. there are an infinite amount of functions that share the same derivative and they all differ by a constant

5/2 x^2 + C defines them all, why?

Answer 18

Because it doesn't effect the derivative it just dissapears

Answer 19

fair enough

so, the question is asking you to really determine a value for C that makes f(10)=0 or when f(-8)=10

Answer 20

so, let x=10

5(10)^2/2 + C = 0, what is C in this case?

Answer 21

-250

Answer 22

right, so

f(2) = 5(2)^2/2 - 250

Answer 23

if f(-8) = 10

5(-8)^2/2 + C = 10, then C = 10-150-10 = -150

f(2) = 5(2)^2/2 - 150

Answer 24

Awesome! Makes sense thanks a lot. Not hard :-)

Answer 25

good luck ;)