Ultimate Mental Calculus

Calculus Level 1

What is the fewest number of derivatives one needs to compute so that $f(x) = 568{ x }^{ 499 }$ becomes zero?

The answer is 500.

1 solution

Andrew Ellinor
Oct 29, 2015

With every derivative, the power on $x^n$ goes down by 1. That means it will require 499 derivatives in order for $568x^{499}$ to have an $x^0$ term, that is to become a constant. Because the derivative of a constant is zero, the desired result will be achieved after one more derivative bringing the total to 500 derivatives.

actually, it could be a trick question, if you take the derivative with respect to not x, it would only take it one time for it to be 0.

Jan Gil - 5 years, 6 months ago

Couldn't you also perform a single derivative calculation by applying the power rule and factorals? making it 499!*568x then you would have your constant and only need two derivatives.

Liam Williams - 3 years, 7 months ago

Thats just short hand for 499 derivatives in one step.

Scott Bartholomew - 2 years, 10 months ago

I think the question is asked incorrectly. The 500th derivative will be 0 for all values of X, but the question asks for f(x) to be zero.

Elliot Rosen - 2 years, 9 months ago

Ultimate Mental Calculus

The answer is 500.

1 solution

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