Question

Test whether the following function is increasing or decreasing.

f(x) = `7/"x" - 3`, x ∈ R, x ≠ 0

Answer 1

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.