Question

Find the values of x for which f(x) = x/x² + 1 is

(a) strictly increasing 

(b) strictly decreasing.

Answer 1

f(x) = x/x² + 1

(a) f is strictly increasing if f'(x) > 0

∴ f is strictly increasing if -1 < x < 1

(b) f is strictly decreasing if f'(x) < 0

∴ f is strictly decreasing if x < -1 or x > 1 

i.e. x ∈ (-∞, -1) ∪ (1, ∞).