Question

What are the coordinates of the turning point for the function f(x) = (x − 2)^3 + 1?

Answer 1

The turning point is (2,1).

Hope this helps!

Answer 2

Answer:

$(2,1)$

Step-by-step explanation:

The given function is,

$f(x) = (x -2)^3 + 1$

Turning point of a graph is the point where the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising).

For a cubic function, the critical point also serves as a turning point.

$\Rightarrow f(x) = (x -2)^3 + 1$

$\Rightarrow f'(x) = 3(x -2)^2$

For critical point,

$\Rightarrow f'(x)=0$

$\Rightarrow 3(x -2)^2=0$

$\Rightarrow (x -2)^2=0$

$\Rightarrow x -2=0$

$\Rightarrow x=2$

Then, $f(2) = (2 -2)^3 + 1=1$

So the critical point or turning point is $(2,1)$