Cubic functions

Question

Find a cubic function of f(x)= ax^3 -bx^2 +cx -d that has a local maximum value of 112 at 1 and a local minimum value of -1184 at 7

Answer 1

Here is a suggestion:

 

f(1) = 112      

f(7) = -1184

 

f'(1) = 0    where f'(x) = 3ax^2 -2bx + c

f'(7) = 0

 

Make those substitutions and you will have four equations with four unknowns (a, b, c, d). Perhaps use rref on a calculator to solve that system.