Finding Critical Points: Where to Look and Why

[appplejack]

Homework Statement

Find any critical point of the following function.

f(t)= 3 — lt-3l, [-1,5]
The answer says it has a critical point where t=3.

Homework Equations

The Attempt at a Solution

f(t)=3 — lt-3l

f(t)=3-t+3, t≥3 f'(t)= -1

f(t)=3-(-t+3), t<3 f'(t) = 1

The function is not differentiable. And it has no critical point. Two cases have different values -> my answer

I remember the definition of critical point is where the derivative of the function either is zero or doesn't exist.

What did I do wrong? and Why is t=3 a critical point?
Thanks.

 

[Dick]

Yes, the function is not differentiable at t=3. As you said. Isn't that the same thing as 'derivative doesn't exist' in the definition of critical point?

 

[appplejack]

oh my. It's right in front of my eyes. I was so locked in on f(t)'= -1 and f(t)'= 1.
Thank you.