quick question (1 Viewer)

[martin310015]

can someone explain to me what monotonically increasing/decreasing means what sort of question it consists and how would u go about to solve it. thanx

 

[Affinity]

intuitively, think monotonic increasing means the graph doesn't go down and monotonically decreasing means it doesn't go up.

the formal definitions are:

if f(x) is monotonically increasing, then f(a) <= f(b) for any a <= b.
if f(x) is monotonically decreasing, then f(a) >= f(b) for any a <= b.
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if f'(x) >= 0 for all x, f is monotonic increasing
if f'(x) <= 0 for all x, f is monotonic decreasing

the questions would generally involve differentiation, where you differentiate a function to prove it's increasing or decreasing.
there might be other things too

 

[Grey Council]

yup, thats right.

although from what i remember:
if f(x) is monotonically increasing, then f(a) < f(b) for any a < b.
if f(x) is monotonically decreasing, then f(a) > f(b) for any a < b.

ie, no 'equal to' sign in the definition.

 

[da_butterfree]

hey whats f(a) and f(b)??

 

[Collin]

From our experiences, our definition bordered around:

f '(x)>0 for monotonically increasing, or f '(x)<0 for monotically decreasing.