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There are several methods of finding the extrema(plural of extremums or in other words minimum or maximum values) of a function.

For now we will analyse the function using the dy/dx of f(x)=y...

We have two functions multiplied together: x and cos(x).

Therefore we have to use the product rule.

First differentiate x and leave cos(x) untouched, so we get 1(cos(x))=cos...

Find the following integral: ∫ x sin(x) dx

This question is a good candidate for the integration by parts method, as it is the product of two different 'parts...

Use the product rule (f'(x)=u'v+uv')

Let u=x²    =>    u'=2x

Let v=log(2x)  =>   v'=2/(2x)  =>    v'=1/x

Therefore f'(x)=2xlog(2x)+x^2<...

If a quadratic equation is of the form : ax^2 +bx +c =0and has roots x1 and x2, then the following statements are true:x1+x2 = - b/ax1x2 = c/aIn our case: x1+x2 = - 8/2 = -4and x1x2 = 1/2Now, x1^...