Question

T or F:
1 - A continuous function on a closed interval always attains a maximum and a minimum value
2 - If y' < 0 for all x in (x,1), then y is decreasing on (0,1).

Answer 1

1 - T
2 - when the first derivative is <0 it's decreasing, right?

Answer 2

for number 2 y is strictly decreasing on (0,1)
This stems from the Mean Value Thereom for derivatives