Search over 10,000 free study notes

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...

Substitute x in terms of y into the first equation:

(2y+6)²+y²=36

Use FOIL to expand the brackets

4y²+24y+36+y²=36 ...

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<...