#6 FRQ AP CALC BC 2022 Part 2

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7
Write the first four nonzero terms and the general term for an infinite series that represents f'(x).
This is part C of the free response question.
How do we answer this question???
8
f'(x) = 1 - x^2 + x^4 - x^6 + ... + (-1)^n*x^2n
Just take the derivative of the given power series!
9
Use the result from part (c) to find the value of f'(1/6).
This is part D of the free response question (the final part)!!
How do we answer this question???
10
f'(x) = 1/(1-(-x^2) = f'(x) = 1/(1+x^2)
f'(x) = 1 - x^2 + x^4 - x^6 + ... + (-1)^n*x^2n + ...
f'(1/6) = 1/(1+(1/6)^2) = 36/37
Since the infinite series for f'(x) is a geometric series, we can apply the geometric series formula!
11
f'(x) = 1/(1-(-x^2) = f'(x) = 1/(1+x^2)
f'(x) = 1 - x^2 + x^4 - x^6 + ... + (-1)^n*x^2n + ...
f'(1/6) = 1/(1+(1/6)^2) = 36/37
Any other questions??
Where is Mr. T???
12

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