# Thread: small confusion in increasing/decreasing function

1. ## small confusion in increasing/decreasing function

A> if a function is f(x) defined in R--> R, STRICLTY increasing and differentiable.. then the derivative of f:
a. May be less than 0 at some x.
b. May be infinite at some x.
c. is greater than or equal to 0 at every x belonging to R
d. is greater than 0 at every x belonging to R

I think the answer is "d" but I am not too sure as it can be 0 also at some point? This is because the second question has confused me a bit.

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B> Consider a strictly decreasing function which is differentiable. Which of the following "may be true" about the derivative of f.

a. derivative > 0 for some x belonging to R
b. derivative = 0 for some x belonging to R
c. derivative = 0 for every x belonging to (a,b) where a<b.
d. derivative >= 0 for every x belonging to R

i think the ideal answer should have been "less than 0" but since that option is not there at all, i am slightly confused.

2. [QUOTE=champrock;220156]A> if a function is f(x) defined in R--> R, STRICLTY increasing and differentiable.. then the derivative of f:
a. May be less than 0 at some x.
b. May be infinite at some x.
c. is greater than or equal to 0 at every x belonging to R
d. is greater than 0 at every x belonging to R

I think the answer is "d" but I am not too sure as it can be 0 also at some point? This is because the second question has confused me a bit.[quote]
Consider the function $f(x)= x^3$.

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B> Consider a strictly decreasing function which is differentiable. Which of the following "may be true" about the derivative of f.

a. derivative > 0 for some x belonging to R
b. derivative = 0 for some x belonging to R
c. derivative = 0 for every x belonging to (a,b) where a<b.
d. derivative >= 0 for every x belonging to R

i think the ideal answer should have been "less than 0" but since that option is not there at all, i am slightly confused.
Now look at $f(x)= -x^3$.

3. got it.

was not taking the inflection points into consideration

thanks a tonne