Question

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

Answer 1

Answer:

The turning points for the given function is (-3,1).

Step-by-step explanation:

The given function is

$f(x)=(x+3)^3+1$

The turning point of a function where the $f'(x)=0$.

$f'(x)=3(x+3)^2$

Equate the first derivative equals to 0.

$0=3(x+3)^2$

$x+3=0$

$x=-3$

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).

Answer 2

The turning point is just the minimum/maximum so the coordinates are (-3,1) which you find from the expression of (x+3)³ + 1