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

Solution:

The given function is f(x) = (x + 3)³ + 1

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

f’(x) = 3(x + 3)²

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

3(x + 3)² = 0

x + 3 = 0

x = -3

At the turning point the x-coordinate is -3.

Substitute x = -3 in the given function

f(-3) = ((-3) + 3)3 + 1

f(-3) = 1

At the turning point the y-coordinate is 1.

Therefore, the turning point is (-3, 1).

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

Summary:

The coordinates of the turning point for the function f(x) = (x + 3)³ + 1 is (-3, 1).