The line y=9x+b is tangent to the graph of f(x) =ax^3 at x=1. Find the values of a and b.

Question

The answer is a=3, and b=-6 according to the answer key. I am confused and could not find this in the book. Please help.

Answer 1

If you take the derivation of a function you get the slope of the function, so f’(x) of ax³ =3ax², substituting 1 for x would give 3a, since slope of tangent line =9; 3a = 9 so a=3

My calculus is a bit rusty, not sure why b would equal-6 but checks out when you graph it.