What are the coordinates of the turning point for the function f(x) = (x − 1)3 − 3?

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 285 People

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

C. (1, -3)

D. (1, 3)

Answered by maham237 @ 25/12/2020

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.

What are the coordinates of the turning point for the function f(x) = (x − 1)3 − 3?

Similar Questions

What are the coordinates of the turning point for the function f(x) = (x + 3)3 + 1?

Find an equation for f 1 x the inverse function

Given the function f(x) = −5x2 − x + 20, find f(3).

Given the function f(x) = 2x, find the value of f−1(32).

Given the function f(x) = log4(x + 8), find the value of f−1(2).

Let g(x) be the reflection of f(x) = x 2 + 3 in the x-axis. what is the function rule for g(x)?

The table represents the function f(x). when f(x) = –3, what is x? –29 –10 –3 –1

F 1 x

Fiona has proved that a function, f(x), is an arithmetic sequence. how did she prove that?

Select the coordinates of two points that are on the line x = 5.

Given the parent functions f(x) = log10 x and g(x) = 3x − 1, what is f(x) • g(x)?

Given the parent functions f(x) = 5x − 1 and g(x) = 3x − 9, what is g(x) − f(x)?

Rewrite f(x) = –(x + 3)2 − 1 from vertex form to standard form.

Area of triangle given 3 points x y z

Rewrite f(x) = 3(x − 2)2 + 1 from vertex form to standard form.

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

All things algebra unit 7 polygons and quadrilaterals answer key

Gina wilson all things algebra 2016 answer key unit 11

Unit 1 geometry basics homework 4 angle addition postulate answers

Unit 6 exponents and exponential functions homework 8 answer key

The manager of a vacation resort believes that the ages

What is 271 403 rounded to the nearest ten thousand

Unit 1 geometry basics homework 3 angle relationships answer key

Homework 2 parallelograms

Why would a prism beat a sphere in a competition?

John wants to send a letter to peter

An artist sells a painting for 20.50 but uses 5.75

Unit 4 congruent triangles homework 1 classifying triangles answer key

Unit 4 congruent triangles homework 2 angles of triangles

Compare the values of the 2s and 5s in 55220