Show that f(x)=1/x does not have extreme values

Nishil Savla

Nishil Savla

Answered question

2022-03-29

Show that f(x)=1/x does not have extreme values in interval (0,1).

Answer & Explanation

star233

star233

Skilled2022-06-09Added 352 answers

Find where the expression 1x is undefined.

x=0

Consider the rational function R(x)=axnbxm where nn is the degree of the numerator and m is the degree of the denominator.

1. If n<m, then the x-axis, y=0, is the horizontal asymptote.

2. If n=m, then the horizontal asymptote is the line y=ab.

3. If n>m, then there is no horizontal asymptote (there is an oblique asymptote).

Find n and m.

n=0

m=1

Since n<m, the x-axis, y=0, is the horizontal asymptote.

y=0

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes: x=0

Horizontal Asymptotes: y=0

No Oblique Asymptotes

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