Respuesta :

kudzordzifrancis
ANSWER

The turning point is

[tex](1,-3).[/tex]


EXPLANATION


The function given to us is

[tex]f(x) = (x - 1) ^{3} - 3[/tex]

At turning point,
[tex]f '(x) = 0[/tex]

So we need to differentiate the given function and equate it to zero.



We using the chain rule of differentiation, we obtain,
[tex]f '(x) =3 (x - 1) ^{2} [/tex]

We equate this to zero to obtain,




[tex]3 (x - 1) ^{2} = 0[/tex]



We divide through by 3.


[tex](x - 1) ^{2} = 0[/tex]

We solve for x to get,

[tex]x - 1 = 0[/tex]


[tex]x = 1[/tex]


We substitute this x-value in to the function to obtain the corresponding y-value of the turning point.





[tex]f(1) = (1- 1) ^{3} - 3[/tex]




[tex]f(1) = 0 - 3[/tex]


[tex]f(1) = - 3[/tex]

Therefore the turning point is


[tex](1,-3)[/tex]

C is the correct answer.

Answer:  C. (1, -3)

Step-by-step explanation:

Given function,

[tex]f(x) = (x - 1)^3 - 3[/tex]   -------(1)

By differentiating the above equation with respect to x,

[tex]f'(x) = 3(x - 1)^2 - 0[/tex]

[tex]f'(x) = 3(x - 1)^2[/tex]

At the turning point of the function f(x),

f'(x) = 0

⇒ [tex]3(x - 1)^2 = 0[/tex]

⇒  [tex](x - 1)^2 = 0[/tex]

⇒ [tex]x - 1 = 0[/tex]

⇒ [tex]x = 1[/tex]

By substituting this value in equation (1),

We get,

f(x) = - 3

Hence, the turning point of the function f(x) is (1,-3).

⇒ Option C is correct.

Otras preguntas