Is a decreasing function's derivative also decreasing?

[zorro]

Homework Statement

Consider the following statements S and R
S : Both sinx and cosx are decreasing functions in the interval (π/2,π)
R : If a differentiable function decreases in an interval (a,b), then its derivative also decreases in (a,b)

Which of the following is/are true?
a) Both S and R are wrong
b) Both S and R are correct but R is not the correct explanation of S
c) R is wrong
d) S is correct

The Attempt at a Solution

S is correct.
I have doubt regarding R.
A function is decreasing iff its derivative is less than 0. I am confused between the 'decreasing of derivative' and 'derivative being less than 0'. Are both same?

I think b and d are correct.

 

[micromass]

S is indeed correct.
Now, you said that a function decreases iff it's derivative is less than 0. Now, can you find a function which is less than 0, but increases nonetheless?

 

[HallsofIvy]

Consider $f(x)= x^2$ on [-1, 0]. It is decreasing. What is its derivative. Is it decreasing also?

 

[zorro]

I got it. Thanks
The answers are c) and d)