I have a problem where I am given the derivative of a function, asked to graph it, then state where it is increasing or decreasing using Mathematica. f'(x)=(x^2-3^x)/2x 0<x<4

I've tried the line of code increasing: Reduce[h'[(x^2 - 3^x)/2 x] > 0 && 0 <= x <= 4, x], however I just receive an error saying that 6 is not a valid variable. I'm really not sure what to do and would appreciate any advice.

  • 1
    $\begingroup$ When I see an error message that says something (like 6) is not a valid variable, it usually turns out to be that I inadvertently set my variable to some value. In this case, with x being the only variable, Clear[x] should fix the problem. By the way, h'[(x^2 - 3^x)/2 x] is not what you want to compare to zero. Also, is the denominator supposed to be 2 or 2x? Just wondering. $\endgroup$
    – LouisB
    Commented Jul 4 at 18:46

1 Answer 1

Reduce[(x^2 - 3^x)/x > 0]

$-\frac{2 W\left(\frac{\log (3)}{2}\right)}{\log (3)}<x<0$

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