Question

Find the critical numbers if they exist. Explain in a sentence how you do it.
f(x) = x

Answer 1

Find the derivative of f(x) which is f'(x). Set f'(x) equal to 0 and solve for x. Those x values will be critical numbers. 8)

Answer 2

The derivative of f(x)=x is 1. So are there any critical numbers?

Answer 3

Nope, because the function 'x' is always increasing. It doesn't change slope at any time.

Answer 4

Err, so yes, there are no critical numbers lol.

Answer 5

I meant to say it doesn't change direction at any time. A change in the direction of a function will result in a critical number at the point in change. But this is too much info for right now I guess lol.

Answer 6

Thank you, can you help me find the critical numbers of f(x) = |2 x+3|, I found the derivative to be: (4x+6)\((sqrt(2 x+3))^2)

Answer 7

Is that abs(2x+3)? I thought this wasn't differentiable, at least at the vertex D:

Answer 8

Hmm, I'm forgetting some rule I think, my stupidity. But the derivative you have is correct.

Answer 9

Yes it is an absolute value. I need to find the critical points I am also given this graph:

Answer 10

Hmm, hold on. This might be a trick question. I'm not sure if an absolute value function has critical numbers.

Answer 11

Wolfram Alpha agrees. Are you sure that's the problem?

Answer 12

yes that is the problem, Problems 3--5. The following functions are defined for all x. Find the critical numbers if they exist. Explain in a sentence how you do it.
f(x) = |2 x+3|

Answer 13

Also, I found this solution someone gave for this problem somewhere:
|u| = √u^2 so let’s let u = 2x+3.
F(x) = y = √u^2
Chain Rule: f’(x) = (dy/du)(du/dx): [u(u’)]/|u| --> u(2)/ √u^2 = (2x+3)(2)/|2x+3|
F’(x) = 2(2x+3)/|2x+3| so -2 and 2 are critical points.

Answer 14

You can do the math and it might give you an "answer," but absolute value functions do not have critical numbers. It is not differentiable at its vertex, where the only critical number WOULD exist.