Find a formula for the following function.
A cubic polynomial with a local maximum at x = 7, a local minimum at x = 9, a y-intercept of 4, and an x^3 term whose coefficient is 1.
from the given info we know that the function looks like
$\displaystyle f(x)=x^3+ax^2+bx+4$ so taking the derivative we get
$\displaystyle f'(x)=3x^2+2ax+b$
max and min points occur when the dervitive is zero so
$\displaystyle f'(7)=0=147+14a+b$ and $\displaystyle f'(9)=0=243+18a+b$
Solving this system for a and b gives us the polynomial
we get $\displaystyle a=-24 \mbox{ and } b=189$
So we get $\displaystyle f(x)=x^3-24x^2+189x+4$
I hope this helps
Good luck