Verified Answer :

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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.

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.

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