Fundamental Theorem of Calculus

[inter060708]

Homework Statement

F(x) = ∫ cos (1+t^2)^-1) from 0 to 2x - x^2

Determine whether F has maximum or minimum value

Homework Equations

The Attempt at a Solution

I tried finding
F'(x) = Dx (∫ cos (1+t^2)^-1) from 0 to 2x - x^2)
= (2-2x)cos[(1+(2x-x^2))^-1]

What do I do next? equate F'(x) = 0 and find F''(x) ?

Please help. Thank you.

 

[chiro]

Hey inter060708 and welcome to the forums.

Turning points happen when the derivative is zero, and the second-derivative (unless it's an inflexion point) will determine whether something is a minimum of maximum based on the sign.

Remember that the second derivative says how fast the derivative is changing, so if it is negative then it means you have a maximum and if it's positive it means a minimum since the derivative (which is the rate of change) will be either 'going negative' or 'going positive'.

So the first thing you need to do is find F'(x) = 0 and take it from there.