What is meaning of increasing and decreasing function?see the marked question?

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1 Answer
Jake M.
Jul 18, 2018

B

Explanation:

A strictly decreasing function means that if you plug in a greater value, you get a smaller value, i.e.
#forall a > b, f(a) < f(b)#

A good example of this might be #1/x#. It decreases constantly.

The reason we say strictly increasing/decreasing is that we can imagine a function which decreases mostly, then flattens out and then increases/decreases again. A good example of this is #x^3#. It increases from the left, then at zero it goes flat, then it increases again.

This isn't strictly increasing but strictly non-decreasing or just non-decreasing since it is flat for a point.

The way this relates to derivatives is if we think about the limit definition of a derivative:
#f'(a) = lim_(hto0)(f(a+h) - f(a))/(h) #

For an increasing function, #h>0# so #f(a+h)>f(a)#, so #f'(a) > 0 forall a#.

This means the answer to the above question is B. We know that it must be negative since it is decreasing and it cannot be zero since then it wouldn't be strictly decreasing.

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