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Let f(x) = 2kx and g(x) = kx^2, where k is a constant. Is there a value of k >1 such that the averages of f and g are equal on [1, k]?
I tried writing it out using formula for avg of a function,
1/k-1 integ(2kx) from 1 to k = 1/k-1 integ(kx^2) from 1 to k
Expanding, I got 2k^4 - 6k^3 + k = 0.
I am not allowed to use calculators in my course, and the solutions for k are decimal values that I cannot understand how to get without a calc.
Or am I doing this wrong and there is no k?
Thanks
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