I Can't Differentiate All Day!

Calculus Level 2

Let $y=f(x)$ be a function in $x.$ Also, let $y^{(n)}$ denote the $n^\text{th}$ derivative of $y$ with respect to $x.$ If $y^\text{(100)}=y^\text{(101)},$ which of the following can possibly be $y=f(x)?$

y=x^{99}

y=x^{100}

y=x^{101}

y=x^{102}

1 solution

Jess Late
Apr 20, 2016

when f(x)=x^99 the 99th derivative will be a constant (it doesn't matter which one) so the 100th derivative will be zero because the derivative of a constant equals zero. Zero is also a constant so the 101st derivative also equals zero (using the logic shown above).

therefore f^100(x) = 0 = f'101(x)

My reasoning as well (:

Andrew Tawfeek - 5 years, 1 month ago

I Can't Differentiate All Day!

1 solution

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