Maharashtra State BoardHSC Commerce 12th Board Exam
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Show that function f(x) =x - 2x + 1, x ≠ -1 is increasing. - Mathematics and Statistics

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Sum

Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.

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Solution

f(x) =`("x - 2")/("x + 1")`, x ≠ 0

For function to be increasing, f '(x) > 0

Then f '(x) = `(("x + 1") "d"/"dx" ("x - 2") - ("x - 2") "d"/"dx" ("x" + 1))/("x + 1")^2`

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

`= 3/("x + 1")^2` > 0       ....[∵ (x + 1) ≠ 0, (x + 1)2 > 0]

Thus, f(x) is an increasing function for x ≠ - 1.

Concept: Increasing and Decreasing Functions
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 4 Applications of Derivatives
Miscellaneous Exercise 4 | Q 4.3 | Page 114
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