# Ap Calculus Questions And Answers

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2003 AP Calculus BC Free Response Answers?

Okay I am working on the 2003 AP Calculus BC Free Response question #4 http://www.collegeboard.com/prod_downloads/ap/students/calculus/calculus_bc_frq_03.pdf

I know you can “askmrcalculus” and get the answers and I understand both a) and b) but I don’t understand either c) or d). I don’t understand Mr. Calculus’ answers for c or d either so…. Can anyone explain?

I sure can.

For part c, they’re asking for the equation of a line tangent to the graph f at the point x = 0

But, we’re not given f. We’re given the derivative of f, which makes things a lot easier for us.
f'(x) = slope of f at the point x
So, looking at the f’ graph, we see that the slope is -2 (the y-value, when x = 0, y = -2)

We can plug this into the equation for a tan line

(y -3) = -2(x-0)

So, the answer for c) is

y – 3 = -2x

For part d, they’re asking for f(-3). Unfortunately, we’re not given the f graph, so we have to find f(-3) manually.

The integral from -3 to 0 of f(x) will give us f(-3)

But we don’t have the function, so we have to manually find the area under the graph.

By finding the area of the two triangles between -3 and 0, and adding them up (area under the graph = negative) we find that it is equal to -1.5. But, we are told that f(0) = 3, so we have to subtract -1.5 from 3, so we find that
3 – (-1.5) = 4.5

The second part of part d is gone about the same way, you find the area between the x axis and the curve, and then add 3 to it. Finding the area is a bit tricky, though.

First you have to find the area of the rectangle under the x axis from 0 to 4. That is b x h = 2 x 4 = 8

From there, we have to subtract the semicircle from that to find the area left over. Area of a circle = pi r^2
Area of a semicircle = 1/2 pi r^2

Looking at the graph we see that r = 2, so the area is

1/2 pi x 4 = 2pi

Now we subtract 2pi from 8, and find that the area remaining is 1.71, but since this area is UNDER the graph, it is negative. 1.71 is not the answer, however, we still need to add three to it. Our final answer is 1.283

I really hope this helped.