are my answers correct?

Question

a. a function changes from a decreasing interval to an increasing interval

-we can conclude that there is a local minimum

b. lim x approaching 0⁺ f(x) = -∞ lim x approaching 0^- f(x) = ∞

-we can conclude that all numbers taken from the positive direction will continuously equal to negative numbers and all numbers taken from the negative direction will continuously equal to positive numbers

c. if the maximum of the function y = x² -4x + 21 occurs at x = 2, what are the coordinates of the maximum point?

-(2,17) because 2² - 4(2) + 21 = 17

d. when finding one-sided limits what does 0⁺ imply?

-it implies that the limit is meant to be taken only from the positive direction

e. when does a limit not exist?

-a limit doesn't exist when the one sided limits exist and are not equal

f. what conditions must be met if a function is said to be continuous?

1. it must be defined at that point
2. its limits must exist at the points
3. the value of the function at that point must equal the value of limit at that point

Answer 1

For b), I would say that as x approaches zero from the right, the function values decrease without bound toward negative infinity. As x approaches zero from the left, the function values grow without bound toward positive infinity.

For e), I would remove "exist and" and just say "when the one sided limits are not equal"