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*not

But the derivative of 1/x^(3/4) is -3/(4*x^(7/4)). As x approaches infinity doesn't it become zero?

hmmm, but still. it would be -3/infinity.

Yes as it approaches infinity, the derivative is 0.

So wouldn't it not satisfy the requirement of the test: "An+1 < An" in other words, decreasing?

It doesn't say the derivative decreases, it says the original function decreases.

well, if the slope is negative, the function is decreasing.

My work points to no, but the answer key says yes. So...

Is there another way to test out this requirement? Derivative was the only way I could think of.

So, are you stuck because of the An+1 < An part of the alternating series test?

Yeah

oh, plugging in n+1 for n and comparing would work right?