If f (x) = ax ^ 3 + 3x ^ 2 + 2 and f '(- 1) = 4, then the value of real number a is equal to? f'(x)=3ax²+6x f'(-1)=3a-6=4 A = 10 / 3 what you have done, but still don't understand. How can you calculate f '(x)?

If f (x) = ax ^ 3 + 3x ^ 2 + 2 and f '(- 1) = 4, then the value of real number a is equal to? f'(x)=3ax²+6x f'(-1)=3a-6=4 A = 10 / 3 what you have done, but still don't understand. How can you calculate f '(x)?

f'(x)=[f(x+△x)-f(x)]/△x
={[a(x+△x)²+3(x+△x)²+2]-(ax³+3x²+2)}/△x
=3ax²+3ax*△x+a△x²+6x+3△x²
Δ x tends to zero
So f '(x) = 3ax & sup2; + 6x