Answer Check please!

A

alexandra.vo

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Is some able to check my answer plz! Thankyou!
 

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The answer that you selected is incorrect.
Go back, study the graph carefully.
What part of the area under the curve is actually shaded?
 
Ok, after looking again at the graph the shaded part looks to travel from b to a. Therefore I'm thinking its either answer b or d. I'm taking d as my answer?
 
I guess the shaded horizontal area runs from 0 to a , therefore it leads me to believe that C is the answer?
 
Yes option A would be all the area between the x-axis and the the curve between x=0 and x=a.
You don't want this whole area, you want to subtract the area of the white rectangle. This rectangle has a base of a, height of b, and so area of ab.
Yes C is correct.
 
Ok thankyou so much for your help, appreciate it! I also have one more graph question i'm confused about another graph question. After looking at the graph I think b is the answer as x would have to be bigger than -2 but less than 2 for f′(x)>0. Is that correct?
 

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It means to me that the derivative of x has to be greater than zero? Therefore would that mean D is the answer? If not, i'm stuck :oops:
 
Yes the derivative is greater than 0. Graphically that means that the graph has a positive gradient and therefore slopes upwards.
So we can eliminate B and C because the graph slopes downwards in that middle section of the graph.
Now D includes 2 and -2 (by the = sign attached to < and >), but A excludes 2 and -2 (no = sign attached).
Is f '(x)>0 when x=-2 or x=2? What is f '(x) when x=-2 and x=2? So do we want to include -2 and 2 in your answer or not?
 
Just draw tangent lines and see where the slope of the tangent lines are positive.
 
Ok thankyou! I'm thinking that we don't want to include -2 and 2 because the slope is decreasing at those points? So I think A?
 
At x=-2 and 2, the gradient is 0 because the tangents there are horizontal. So we don't want to include -2 and 2. "A" is correct, but your reasoning is wrong.
 
I would object to all the choices on the ground that there is NO "f(x)" shown on the graph so we cannot know if any of them are correct!
 
HallsofIvy said:
I would object to all the choices on the ground that there is NO "f(x)" shown on the graph so we cannot know if any of them are correct!
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Excellent point. I missed that one. I got a few professors upset with me for saying things like this on exams. I truly respected my professors and I felt that I had no right at all to rewrite their exam the way they meant to write it. So I just stated why the problem was not possible to solve.
 
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