Find a formula for the following function. A cubic polynomial with a local maximum at x = 3, a local minimum a

Question

x = 5, a y-intercept of 5, and an x^3 term whose coefficient is 1.

Answer 1

with your addtinional remarks the formula is

x^3+ax^2+bx+5 (since the intercept on y is 5, otained for x=0)

Its derivative is dy/dx =3x^2+2ax+b
At the local minima the derivative equal zero so can be divided by (x-3) *(x-5) = x^2-3x-5x+15 =x^2-8x+15
as the first term of derivative is 3x^2 it must look as
3x^2-24x +45
you have 2a=-24 so a=-12 and b=45

result y =x^3-12x^2+45x+5