Answer:
[tex](2,1)[/tex]
Step-by-step explanation:
The given function is,
[tex]f(x) = (x -2)^3 + 1[/tex]
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.
[tex]\Rightarrow f(x) = (x -2)^3 + 1[/tex]
[tex]\Rightarrow f'(x) = 3(x -2)^2[/tex]
For critical point,
[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]
Then, [tex]f(2) = (2 -2)^3 + 1=1[/tex]
So the critical point or turning point is [tex](2,1)[/tex]
