Question

Find f(x) if f(0)=1 and the tangent line at (x, f(x)) has slope 7x.

Its been a long while since I have done one of these somebody please help!!

Answer 1

is the slope \(7\) ?
\(7x\) is not a slope

Answer 2

maybe... the problem says 7x... let me see if I can send you a screenshot

Answer 3

f'(x) = 7x

Integrate both sides to find f(x).

Put x = 0, y = 1 and find the constant.

Answer 4

oh that is an entirely different question
the anti derivative is \(\frac{7x^2}{2}+C\)

Answer 5

then you can solve for \(C\) since \[f(0)=1=C\]

Answer 6

so it will be \[\frac{ 7x^{2} }{ 2 }+1\]???

Answer 7

yes

Answer 8

do I need to further simplify it?

Answer 9

or leave it as is?