Question

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

Answer 1

Answer:

42

Step-by-step explanation:

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