Question

find f(x) if f'(x)=(9+(-12/x)) and f(2)=3

Answer 1

Integrate.

Integral of 9dx is?

Integral of (-12/x)dx or (-12)(1/x)dx is?

Answer 2

in9dx=9x

Answer 3

Yes....

Integral of (-12/x)dx or (-12)(1/x)dx is?

Answer 4

and -12ln(x)

Answer 5

Right.

Answer 6

So, f(x) = 9x - 12ln(x) + C

You were given the initial condition of f(2) = 3....

so: 3 = 9(2) - 12ln(2) + C

C = ?

Answer 7

-15+12ln(2)?

Answer 8

Yep.

So: f(x) = 9x - 12ln(x) + (-15 + 12ln(2)).

That's what you wanted right?