00:01
In this problem we are given with the graph of the function f of x.
00:05
In part a, we are as to find the critical values for which the value of f dash of x is equal to 0.
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Before finding the critical value from the given graph, we should know what do we mean by critical value of a function.
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Critical value of a function can be found using two different methods.
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First method is we find the value of f dash of x and v.
00:33
Equate that to 0.
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The values of x that satisfies this equation becomes the critical value of the given function.
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The second method is we find when the value of f dash of x does not exist and the values of x for which f dash of x becomes undefined or also called the critical value of the given function.
01:02
In part a, we need to find the value of x, for which f dash of x becomes zero.
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And one more thing what we need to know is, we find critical values to find the maximum or minimum value of the function f, meaning the function f reaches its maximum or minimum value at their respective critical values alone.
01:29
So we have the graph of f of x and from the graph we can figure out where the function reaches maximum value or minimum value and among them we need to find which of them satisfies this condition.
01:45
If we take a look at our graph, what we can say is when x is equal to minus 3, the function reaches local minimum.
01:56
So, x is equal to minus 3 will be our value of x for which f dash of x becomes 0.
02:04
Why? because the curve at x, is equal to minus 3 looks smoother.
02:10
So we can find the value of f dash of x at this particular point which is nothing but x is equal to minus 3.
02:17
So this is the answer for the first part of the problem...