A True or False Common Sense Question
Geometry
Level
3
True or false?There are infinitely many functions that are not equivalent to a trigonometric function(or a trigonometric function itself)that when differentiated infinitely many times the derivative is not 0.
False
Impossible to Solve
True
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1 solution
For any real number n the derivative of n^x is n^x multiplied by ln(n).When you take the derivative of that ln(n) "becomes" ln(n)^2.If n is greater than or equal to e,than the constant term trends towards infinity which is not 0. Hence the answer is true.