Global Extrema of a Function: Finding the Maximum and Minimum Values

oswald88
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Homework Statement



Find max and min value of the function

Homework Equations



attached.

The Attempt at a Solution



no graph, because roots aren't real numbers.
 

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As you've found, there are no real values of x where f'(x)=0...what does that tell you about the existence of local maxima/minima? Are there other types of extrema? Where might they occur?
 
no idea! need imaginary graph? maybe there isn't any max or min.. so the exercices question is meanless.
 
You need to read the section n your textbook on global extrema.
 

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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