Find a cubic function, in the form below, that has a local maximum value of 4 at -4 and a local minimum value of 0 at 2.

Question

Find a cubic function, in the form below, that has a local maximum value of 4 at -4 and a local minimum value of 0 at 2.

 

f (x) = ax^3 + bx^2 + cx + d

Answer 1

Hi Mia,

 

I will get you started.

 

If the function has local extrema at a particular x value, then that number is a critical number, i.e. the first derivative will be zero there.

 

Also when the x value is supplied to the original function the max/min value will be generated.

 

f'(x) = 3ax²+2bx+c

 

f'(-4) = 0

f'(2) = 0

f(-4) = 4

f(2) = 0

 

Substitute those values for x into f(x) and f'(x). This will result in 4 equations with 4 unknowns (a,b,c,d). 

 

Use whatever method(s) you have in your repertoire for solving simultaneous linear equations.