00:01
So in this question, we're going to use the graph of the function f of x displayed below to answer the following question.
00:07
In part a, i want to find the critical values where f prime of x is equal to zero.
00:14
So if f prime of x equals zero, that means the slope of my tangent line is going to be equal to zero.
00:23
And i see a couple of places where that's going to happen.
00:27
Looks like that's at x equals zero.
00:29
And it also looks like it's here at x equals 5.
00:36
So i would say that my f prime of x is equal to 0, the slope of my tangent line is equal to 0 at x equals 0 and x equals 5.
00:46
In part b, i want to find the critical values where f prime of x does not exist.
00:54
Now, how might f prime not exist? f prime will not exist if f either has a vertical tangency or a sharp point so i notice that f has a vertical tangency here at x equals two and i know that the graph of this function f has a sharp point at x equals eight and so my f prime does not exist at x equals two and x equals two and x equals eight this time in part c, finding x coordinates of the relative maxima of the function f of x.
01:38
So the relative maxes are the tops of the hills.
01:43
And so there appears to be a relative maximum this time right here at x equals zero...