You should write the function (derivative of the integral) as:
(x^2-4)/(1+cos(x)^2)
this is zero for x = +/- 2.
Find and classify the relative maxima and minima of f(x) if f(x)= defint a=0 b=x
function= t^2-4/(1+cos(t)^2) dt
x^2-4/(1+cos(x)^2)= 0
x^2-4=0
x^2=4
x= +/- 2
So I got relative maximum as -2 and 2. And relative minimum as zero. However, when I graph it on Wolfram, it gives me more maxima like +/-4.99, +/-7.999, etc. How did they get those values? Can someone please explain that to me? Thank you for your time.
Sorry I wrote the wrong variable in the last posting (this is a correction).
I got +/-4.99 and +/-7.99 when I typed the keyword 'local maximum x^2-4/(1+cos(x)^2)'
into the equation box. It just gave me a list of maxima.
2 answers
you don't want the minima and maxima of (x^2-4)/(1+cos(x)^2)
That is not f(x). It is f'(x). So, the minima and maxima of f(x) occur when (x^2-4)/(1+cos(x)^2) = 0.
That is not f(x). It is f'(x). So, the minima and maxima of f(x) occur when (x^2-4)/(1+cos(x)^2) = 0.