The function f is given by f(x) = (x^(3) + bx + 6)g(x) where b is a constant and g is differentiable function satisfying g(2) =3 and g'(2)= -1. For what value of b f'(…

Question

The function f is given by


`f(x) = (x^(3) + bx + 6)g(x)`
where b is a constant and g is differentiable function satisfying g(2) =3 and g'(2)= -1. For what value of b f'(2) =0

a. -7
b. -10
c. -12
d. -22
​

Answer 1

d. -22

Explanation:

If F(x) is given by:

`f(x)=(x^(3)+bx+6) g(x)`

The derivative is given by:

`f'(x)=(3x^(2)+b) g(x)+(x^(3)+bx+6) g'(x)`

if f'(2)=0

`f'(2)=(3(2)^(2)+b) g(2)+((2)^(3)+2b+6) g'(2)=0`

`3(12+b)-(14+2b)=0`

`36+3b-14-2b=0`

`b=-22`