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Test whether the function is increasing or decreasing. f(x) = x-1x, x ∈ R, x ≠ 0, - Mathematics and Statistics

Sum

Test whether the function is increasing or decreasing. 

f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0, 

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Solution

f(x) `= "x" - 1/"x", "x" in "R"`

`therefore "f"'("x") = 1 - (- 1/"x"^2) = 1 + 1/"x"^2`

`∵ "x" ne 0,` for all values of x, `"x"^2>0`

`therefore 1/"x"^2 > 0, 1 + 1/"x"^2` is always positive

thus f'(x)>o , for all x ∈ R

Hence f(x) is increasing function.

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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 4 Applications of Derivatives
Exercise 4.2 | Q 1.2 | Page 106
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