- #1
quincyboy7
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Homework Statement
Find a function, strictly increasing, whose derivative equals zero at TWO places. Find another such function whose derivative equals zero at infinitely many places. These should not be piecewise and should be continuous on all reals.
Homework Equations
f(x)=x^3 has one such spot, at x=0.
The Attempt at a Solution
I can't imagine the answer is a polynomial, since the derivatives of those will have x terms that can equal 0 at only one place (think x^3, x^5, x^7, etc.). Any manipulations of such polynomials make them not strictly increasing, which is another problem.
Sine and cose functions probably can't be made strictly increasing by any manipulations. Inverse functions don't have derivatives equaling zero, I don't think.
E^x and sqrt(x) are both not continuous on both reals and don't have derivative zero anywhere.
I just can't think of anything more in terms of function "families" that could work...any pointers would be great