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Numerade Educator

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Problem 19 Easy Difficulty

For the function $ f $ graphed in Exercise 18:

(a) Estimate the value of $ f'(50) $.
(b) Is $ f'(10) > f'(30) $?
(c) Is $ f'(60) > \dfrac{f(80) - f(40)}{80 - 40} $? Explain.

Answer

a) $\approx 26$
b) The given statement is not true
c) The given statement is true

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Video Transcript

I mean? So I will try to explain this and then you'll have to look at your graph. This is asking you to approximate the slope At x equals 50. So whatever your graph is, Again, I don't know what it is, but you're going to go over to 50 on the X-axis, find your graph. And if this was my graph, you're going to estimate the slope. So draw a tangent line and then estimate the rise over the run. I don't know exactly what it is because I don't have your graph. But that's what it's asking you to do. And then it's asking you if F prime of 10 is greater than f prime of 30. Again, this is asking you is the slope At x equals 10, more than the slope At x equals 30. So in my particular graph, if this was 10 And this was 30, it looks like This, my particular situation would be no, because the line appears to be less steep at 10 than it does at 30. So you're looking for the steepness or the slope of your graph, and then for the last one, you're being asked to find the average rate of change, also known as the slope. So the slope between the points 80 f. of 80 and 40 FA 40. Again, I don't have your graph, so I can't actually figure that out for you, But you'll go to 80 on your graph. Find the Y value, go to 40 on your graph, find the y value, then plug them into your equation and find the slope.