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

Solution:

The given function is f(x) = (x + 2)³ - 4

The turning point of a function where the f’(x) = 0

f’(x) = 3(x + 2)²

To find the value of x, equate the first derivative equal to 0.

3(x + 2)² = 0

x + 2 = 0

x = -2

At the turning point the x-coordinate is -2.

Substitute x = -2 in the given function

f(-2) = ((-2) + 2)³ - 4

f(-2) = -4

At the turning point the y-coordinate is -4.

Therefore, the turning point is (-2, -4).

---

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

Summary:

The coordinates of the turning point for the function f(x) = (x + 2)³ - 4 is (-2, -4).