What are the coordinates of the turning point for the function f(x) = (x + 2)3 - 4?

The coordinates of the turning point for the function f(x) = (x + 2)3 – 4 are (-2, -4). I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

Answer Link

InesWalston InesWalston · Answer 2 · 2018-12-03T13:12:11+01:00

Answer:

The coordinates of the turning point will be (-2, -4)

Step-by-step explanation:

The given function is

[tex]f(x) = (x + 2)^3 - 4[/tex]

The turning point is a point where the function goes from increasing to decreasing or reciprocally.

At the point where the gradient or slope of the curve is 0, that is the turning point.

Gradient is the first derivative of the function.

so,

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

Then,

[tex]\Rightarrow f'(x) = 0[/tex]

[tex]\Rightarrow 3(x + 2)^2 = 0[/tex]

[tex]\Rightarrow (x + 2)^2 = 0[/tex]

[tex]\Rightarrow x + 2 = 0[/tex]

[tex]\Rightarrow x=-2[/tex]

At x= -2, f(x) will be

[tex]f(x) = (-2+ 2)^3 - 4=0-4=-4[/tex]

So the coordinates of the turning point will be (-2, -4)