Graph sketching, continuity, differentiation - Is this right?
(I would appreciate either an explanation as to how to solve the problems, or the correct answer so I could figure out what I did wrong.)
1. Let f(x) =
4-x^2 if x < 2a) Sketch the graph of f.
x^2 - 5x + 6 if 2 < x < 3
x if x > 3
b) At what numbers is f continuous?
- I'm not sure if I did this right, are you supposed to do something with limits to show what numbers are continuous?
(-∞, 2], [2, 3], [3, ∞)
c) At what numbers is f differentiable?
- Again, I've seen in some places where your answer has to include limits. Do you have to use limits in your work or something?
d) Give a formula for f'.
2x if x < 22. Let f(x) = x^3 - 9x^2 + 24x + 3
2x - 5 if 2 < x < 3
1 if x > 3
a) For what values of x does the graph of f have a horizontal tangent
- Okay I have no idea what to do for this one. I tried looking through my textbook and couldn't find anything. If someone could show me how to do this, that would be great.
f''(x) = 9