-8x 20 is a tangent to f(x) x^3 x^2 bx 18 at x=1 calculate the values of a and b

I tried the question but I failed

3 answers

x^3+x^2+bx+18
-8x+20
f = x^3+x^2+bx+18
f' = 3x^2 + 2x + b
f'(1) = 3+2+b = 5+b

Since y = -8x+20 is tangent at x=1, it has the same slope as the curve there. So,

5+b = -8
b = -13

I have no idea where a comes into play, but maybe you can work it in and include it in the solution.