Question

What are the coordinates of the turning point for the function f(x) = (x - 1)3 - 3? A. (-1, -3)

Answer 1

Answer:  C. (1, -3)

Step-by-step explanation:

Given function,

$f(x) = (x - 1)^3 - 3$   -------(1)

By differentiating the above equation with respect to x,

$f'(x) = 3(x - 1)^2 - 0$

$f'(x) = 3(x - 1)^2$

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

f'(x) = 0

⇒ $3(x - 1)^2 = 0$

⇒  $(x - 1)^2 = 0$

⇒ $x - 1 = 0$

⇒ $x = 1$

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.

Answer 2

ANSWER

The turning point is

$(1,-3).$


EXPLANATION


The function given to us is

$f(x) = (x - 1) ^{3} - 3$

At turning point,
$f '(x) = 0$

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



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

We equate this to zero to obtain,




$3 (x - 1) ^{2} = 0$



We divide through by 3.


$(x - 1) ^{2} = 0$

We solve for x to get,

$x - 1 = 0$


$x = 1$


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





$f(1) = (1- 1) ^{3} - 3$




$f(1) = 0 - 3$


$f(1) = - 3$

Therefore the turning point is


$(1,-3)$

C is the correct answer.