Given ##f(x)=3x^5-5x^3##, find all critical points.

angela107
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Homework Statement
Given ##f(x)=3x^5-5x^3##, find all critical points and identify any local
max/min point.
Relevant Equations
n/a
Is my work right?
Screen Shot 2020-05-26 at 11.45.14 PM.png
 
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Check your factorisation of y'' (but you do not seem to have used it).
Other than that, looks fine.
 
Last edited:
I think it's fine, but I agree with @haruspex that you have to check the factorisation of ##y''##.
Just a friendly reminder: there are critical points as well where the derivative doesn't exist. In this case, the first derivative exists for every ##x##, so you don't have to matter.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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