Question

what are the critical points of x(2x+1)^(1.2)

Answer 1

what are you defining by the term 'critical point'?

Answer 2

it should be to the 1/2 power

Answer 3

where the derivative of x = 0. My question is I got -1/3 as a critical point. Is -1/2 also a critical point?

Answer 4

one of the overlooked aspects of critical points is that when the derivative is undefined we also have a critical point.

Answer 5

Right. But since it is an endpoint and the domain is [-1/2, infinity) is -1/2 still a critical point?

Answer 6

x (2x+1)^(1/2)

x' (2x+1)^(1/2) + x (2x+1)'^(1/2)

(2x+1)^(1/2) + x/(2x+1)^(1/2)

ah, a restricted domain, then yes the endpoints are also critical points

Answer 7

Thank you!

Answer 8

2x+1 + x
-----------
(2x+1)^(1/2)



3x+1
-----------
(2x+1)^(1/2)



-1/3, -1/2 are the main critical points, and they both fall within the domian