add 3 and 1
change -2 ---> 2
C. (1, -3)
By differentiating the above equation with respect to x,
At the turning point of the function f(x),
f'(x) = 0
By substituting this value in equation (1),
f(x) = - 3
Hence, the turning point of the function f(x) is (1,-3).
⇒ Option C is correct.
Turning Point is the point where the graph changes its nature i.e. either increasing to decreasing or decreasing to increasing
to find turning point
For critical point
(-2,-4 ) is the turning Point where Function changes its nature
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The coordinates of the turning point will be (-2, -4)
The given function is
The turning point is a point where the function goes from increasing to decreasing or reciprocally.
At the point where the gradient or slope of the curve is 0, that is the turning point.
Gradient is the first derivative of the function.
At x= -2, f(x) will be
So the coordinates of the turning point will be (-2, -4)
The turning point is
The function given to us is
At turning point,
So we need to differentiate the given function and equate it to zero.
We using the chain rule of differentiation, we obtain,
We equate this to zero to obtain,
We divide through by 3.
We solve for x to get,
We substitute this x-value in to the function to obtain the corresponding y-value of the turning point.
Therefore the turning point is
C is the correct answer.
If this is wrong please let me know.
The given function is,
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.
For critical point,
So the critical point or turning point is
f(x) = (x - 2)^3 + 1
Find the derivative:-
f'(x) = 3(x -2)^2 This = 0 at the turning points:-
so 3(x - 2)^2 =
giving x = 2 . When x = 2 f(x) = 3(2-2)^3 + 1 = 1
Answer is (2, 1)