I need help finding the critical points of the function $x^5+x^4-2x^2$, I don't understand, can someone help show me how to find the critical points please
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Hint: Try differentiating $f(x) = x^5 + x^4 - 2x^2$.
Then try to find the values of $x$ at which $f^\prime(x) = 0.$ One such value for $x$ will be clear. Then try to find the second root, by approximating, if necessary.
See for example, the plot of your function close to the origin:
In general, for finding critical points $c$ of a function $f$ (not necessarily a polynomial), the following may help:
Critical point checklist:
Given a function $f(x)$ defined on an interval $J$ and a point $c$ in $J$ in its domain, then...
You take the derivative-what do you get? Then set it to zero. You should have a fourth degree derivative. One root is obvious. There is a second real one that you can only approximate unless you want to solve a messy cubic.