Question

(1 point) Find f'(1) if 6x (f(x))^4 +9x^3 f(x) = 78 and f(1) = -2​

Answer 1

42

Explanation:

`6x (f(x))^(4)+9 x^(3) f(x)=78\\6x (f(1))^(4)+9 x^(3) f(1)=78\\6x(-2)^(4)+9 x^(3) (-2)=78\\f(x) = 6x(16)-18 x^(3)=78\\f'(x)=96-54x\\for x=1: f'(1)=96-54(1)=42`