# Test whether the following function is increasing or decreasing. f(x) = 7x-3, x ∈ R, x ≠ 0 - Mathematics and Statistics

Sum

Test whether the following function is increasing or decreasing.

f(x) = 7/"x" - 3, x ∈ R, x ≠ 0

#### Solution

f'(x) = 7/"x" - 3, x ∈ R, x ≠ 0

∴ f'(x) = (-7)/"x"^2

x ≠ 0, x2 > 0, i.e., 1/"x"^2 > 0, i.e., - 7/"x"^2 < 0

∴ f'(x) < 0 for all x ∈ R, x ≠ 0

Hence, f(x) is a decreasing function, for all x ∈ R, x ≠ 0.

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
Exercise 4.2 | Q 1.3 | Page 106