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Trace or copy the graph of the given function $ f $. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of $ f' $ below it.

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So in this problem were given a graph of a function F. We were asked to trace or copy it. So, first of all, let's get our graph up here. There's X. Here's why. And our graph goes up to some maximum and then comes back down like this. Okay. They were asked to use the method of example 1 to sketch the graph of f prime. This is F F prime, blow it again. We'll have X and Y here. Okay? Yeah. The method says to pick points on here and look at the slopes at those points and use those to determine where we are on the derivative curve. We can see, first of all, if we do appoint a here that this tangent line, right is nearly vertical. So that means that we are at some very positive slope here. Okay? And then if we pick a point be right here on the top of the curve, that's a horizontal, that's a zero slope. So we know that he's going to be here. We know that A. Is up here somewhere for that value of X. Then we pick a grab a point over here, point C. And look at that tangent line that's negative, right? As this is a decreasing curve. And that's at the point where it's the steepest negative. And so that means we're going to have some point C. Down here happening to us, we are negative and we are the steepest negative and notice that this trends on toward zero. So this is C. Okay, so what happens? Well from here, I trend up towards zero from B to C. I got more and more negative like that and from A to B. I came from very positive down to zero. And so there is my graph for the derivative of F.

Oklahoma State University