If 23+7f(x)+4x2(f(x))3=0 and f(2)=−1, find f′(2). f′(2)

Question

If 23+7f(x)+4x2(f(x))3=0 and f(2)=−1, find f′(2).

f′(2)=?

Answer 1

23 + 7 f(x) + 4 x² f³(x) = 0

drive the equation

0 + 7 f´(x) + 4 [ 2x f³(x) + x² * 3 f²(x) f´(x) ] = 0

7 f´(x) + 8 x f³(x) +12 x² f²(x) f´(x) = 0 , at x=2 f(2) = -1

7 f´(2) + 8 (2)( -1)³ + 12 (2)² (-1)² f´(x) = 0

7 f´(2) - 16 + 48 f´(2) = 0

55 f´(2) = 16

f´(2) = 16 / 55