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!!

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!!

anonymous · Answer

is the slope $7$ ?
$7x$ is not a slope

anonymous · Answer

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

ranga · Answer

f'(x) = 7x

Integrate both sides to find f(x).

Put x = 0, y = 1 and find the constant.

anonymous · Answer

attachment

anonymous · Answer

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

anonymous · Answer

then you can solve for $C$ since $$f(0)=1=C$$

anonymous · Answer

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

anonymous · Answer

yes

anonymous · Answer

do I need to further simplify it?

anonymous · Answer

or leave it as is?