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Calculus
A Further Function Puzzle (
Posted on 20070119
)
Define f(x+y) = f(x) + f(y)  1 for all real x and y such that f(x) is differentiable for all values of x with f ’(0) = cos A.
Determine whether or not the value of f(1) – cos A is equal to 2.
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Submitted by
K Sengupta
Rating:
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A solution
Comment 1 of 1
A was not defined, so I assume A is a constant
f(x) = cos(A)*x + 1
f(x+y) = cos(A)*(x+y) + 1
= [cos(A)*x + 1] + [cos(A)*y + 1]  1
f'(x) = cos(A) for all x, so f'(0) = cos(A)
f(1) = cos(A) + 1 so f(1)  cos(A) = 1 (not 2)
Posted by
Larry
on 20070119 22:53:11
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