How can you identify critical points by looking at a graph?
Please read the explanation.
Definition of a Critical Point:
A continuous function

#color(blue)(f'(x)=0# 
#color(blue)(f'(x)# is undefined.
A critical point can be a local maximum if the functions changes from increasing to decreasing at that point OR
a local minimum if the function changes from decreasing to increasing at that point.
Let us consider the Sin Graph:
One Period of this graph is from
The graph does not go above
View the graph below:
Note that the graph starts from
Observe that the points
We have a maximum at the point
Critical Points:
Formula :
Note that the distance between the points:
are all equal and there are four of them.
Hence,
and the Critical Points are
and the distance between any two critical point is
Hope this helps.
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Critical points on a graph can be identified by examining where the derivative of the function is zero or undefined. These points include local maximums, local minimums, and points of inflection. To find critical points, locate where the derivative changes sign or is equal to zero. Then, analyze the behavior of the function around those points to determine their nature.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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 How do you find critical points on a graph?
 Is #f(x)=(x3)^3+3x^22x # increasing or decreasing at #x=0 #?
 Given the function #f(x)=x/(x+9)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,18] and find the c?
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