contestada

The function f is given by
[tex]f(x) = (x^{3} + bx + 6)g(x)[/tex]
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
​

Respuesta :

Answer:

d. -22

Step-by-step explanation:

If F(x) is given by:

[tex]f(x)=(x^{3}+bx+6) g(x)[/tex]

The derivative is given by:

[tex]f'(x)=(3x^{2}+b) g(x)+(x^{3}+bx+6) g'(x)[/tex]

if f'(2)=0

[tex]f'(2)=(3(2)^{2}+b) g(2)+((2)^{3}+2b+6) g'(2)=0[/tex]

[tex]3(12+b)-(14+2b)=0[/tex]

[tex]36+3b-14-2b=0[/tex]

[tex]b=-22[/tex]

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