
Cubic polynomials
Eh. Here's the problem:
"A cubic polynomial is given by $\displaystyle f(x)=ax^3+bx^2+30x+k$ where a, b, and k are constants. The function f(x) has a local minimum at (1,10) and a point of inflection at x=2.
a) Find the values of a, b, and k.
b) Use the second derivative to verify that (1,10) really is a local minimum for your function.
c) Find the location of any local maximums for your function. Verify that they are indeed a local maximum."
Here's what I've done so far..
I've found the first derivative, $\displaystyle f(x)= 3ax^2 + 2bx + 30$
and the second derivative, $\displaystyle f(x)= 6ax + 2b$.
I then plugged the value of x=1 into the first derivative, getting $\displaystyle 3a2b+30$.
I also plugged the inflection point of x=2 into the second derivative and got
$\displaystyle 12a+2b$.
From there, I can't seem to remember what to do. Help, please? D:

solve the following linear equations :
$\displaystyle f(1)=a(1)^3+b(1)^2+30(1)+k=10$
$\displaystyle f'(1)= 3a(1)^2 + 2b(1) + 30=0$
$\displaystyle f''(2)= 12a + 2b=0$
to get the value of a, b, and k.