Question

find the min and max of the function on the given interval by comparing values at the critical points and endpoints.
(1+x^2)^(1/2) - 2x, [0, 1] find the min and max of the function on the given interval by comparing values at the critical points and endpoints.
(1+x^2)^(1/2) - 2x, [0, 1] @Mathematics

Answer 1

Ok first thing to do is find the derivative and set it equal to zero.. These are your critical points.

Answer 2

\[\sqrt{1+x^2} - 2x\]

Answer 3

\[\frac{1}{2\sqrt{1+x^2}}* 2x - 2\]

Answer 4

\[\frac{2x}{2\sqrt{1+x^2}} - 2\]

Answer 5

or \[\frac{x}{\sqrt{1+x^2}} - 2\]

Answer 6

now set that equal to zero and solve for x

Answer 7

that's where i was having problems. every time i tried that, i got to x equaling the square root of a negative number

Answer 8

Yeah im getting complex solutions.. So there are no critical points. So just compute \[f(0)\] and \[f(1)\] These are your endpoints of your closed interval.

Answer 9

ok thanks a lot!