Differential calculus using chain rule, product rule and quotient rule.

Question

Im unsure on how to do this question.

this is for homework and its a complex question.

the question is

for f(x)=ax(x²-b) where both a and b are constants, f(x)=8b when x=4, f'(x)=15a when x=3. Find constants a and b to determine f(x) and f'(x)

Answer 1

Multiply out f(x) = ax³ - bax

Take the derivative: f'(x) = 3ax² - ba

Plug in

f(4) = a(4)³ - 4ba = 8b or 64a - 4ba = 8b (solve for b in terms of a)

f'(3) = 3a(3)²-ba = 15a or 27a² - ba = 15a (plug in for b in this equation.

I'll leave the algebra to you. You actually didn't need any of the differentiation rules if you multiply the function out