tangent lines and slopes and integrals... so confused

[Guest]

I just posted a topic about integrals, I guess I'm really confused...

Anyway, I'm looking for some guidance on this problem. Where to start maybe?

Given that the graph of f(x) passes through the point (2,5) and that the slope of its tangent line at (x, f(x)) is 7x+3, what is f(3)?

 

[skeeter]

got news for you ... this is an integration problem also, and a very easy one to boot.

you know that f(2) = 5, and the slope of the tangent line at any value on the curve is 7x+3 ...

the last statement is telling you that f'(x) = 7x+3.

integrate f'(x), and use the given initial condition, f(2) = 5, to find the function f(x) ... then you can determine the value of f(3).