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# Analyzing mistakes when finding extrema (example 2)

AP.CALC:
FUN‑4 (EU)
,
FUN‑4.A (LO)
,
FUN‑4.A.2 (EK)
Analyzing the work of someone who tried to find extrema of a function, to see whether they made mistakes.

## Want to join the conversation?

• Do we always need to find all critical points? What about functions like
x^3/(x+sin(x)) ?
• Yes you do need to find all the critical points, for example the function you asked x^3/(x+sin(x)) click here to see the graph
https://www.desmos.com/calculator/ue5ryx9hze

If you're asking for regular trig functions then you don't have to find their critical points since they're repeating.
(1 vote)
• Isn't the f' also undefined for x € [0, 1] since the square root can't be negative?
• No, because what f' actually contains is a cube root which is in fact defined for all real numbers since it is an odd root.
• For Step 3, in the third column, first row, the equation reads "`f'(3) = -2 < 0`". Since this is the evalution of the test x-value, x= -3, shouldn't this read "`f'(-3) = -2 < 0`"?