Find f(x) if f'(x) =
7
x4
and f(1) = 4.

Question

Find f(x) if f'(x) =
7
x4
and f(1) = 4.

anonymous · Answer

can you rewrite that please? :D

lgbasallote · Answer

uhhh could you put the "f'(x) =" in one line? izkinda confusing..

anonymous · Answer

how do u rewrite it? lol do i close it then open  it again?

anonymous · Answer

no just re-put your question on this thread

lgbasallote · Answer

or there is an Edit Question link beside Report Abuse

lgbasallote · Answer

on the question itself i mean..

anonymous · Answer

find f(x) if f '(x)= 7/x^4 and f(1)=4

anonymous · Answer

f'(x) = 7/x^4

$$\int\limits_{}^{} f'(x) = \int\limits_{}^{}7/x^4$$

by the fundamental theorem of calculus

$$\int\limits_{}^{} f'(x) = f(x)$$
so:

$$f(x) = \int\limits_{}^{}7/x^4$$

1/x^4 can be rewritten as x^-4, so:

$$f(x) = \int\limits_{}^{} 7x ^{-4}$$

integrating that, we get:

f(x) = (-7/3)(x^-3) + c

f(x) = (-7/3)(1/x^3) + C

f(1) = 4 

so plugging that in:

4 = (-7/3) (1/(1)^3) + C

4 = (-7/3) + C

C = 19/3

our final answer should be:

f(x) = (-7/3)(1/x^3) + 19/3

somebody check my work please!

anonymous · Answer

well the closest answer to yours in my answers is (-7/3) (x^-3) + 19/3 so idk if thats wat u meant

anonymous · Answer

but i appreciate your help!

anonymous · Answer

yes that is what i meant :D