Solving for c: Finding all Values in (a,b)

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Remy Starr
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Homework Statement


Find all values of c in the open interval (a,b) such that f'(x)=0.


Homework Equations


f(x)=(x-2)(x+3)^2 [-3,2]


The Attempt at a Solution

How do I solve this?
 
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I don't see how Rolle's theorem is relevant to solving the problem. All it will tell you is that there is at least one value in the interval where f' is 0. It won't tell you where it(they) is(are). To do that, it seems you simply need to take the derivative, and solve for zero.
 

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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