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Show that is a decreasing function on (0, ∞).
we have
let x1,x2 (0,) We have, x1 > x2
⇒
⇒ f(x1) < f(x2)
Hence, x1 > x2⇒ f(x1) < f(x2)
So, f(x) is decreasing function
Prove that the function f(x) = loge x is increasing on (0, ∞).
Prove that the function f(x) = loga x is increasing on (0, ∞) if a > 1 and decresing on (0, ∞), if 0 < a < 1.
Prove that f(x) = ax + b, where a, b are constants and a > 0 is an increasing function on R.
Prove that f(x) = ax + b, where a, b are constants and a < 0 is a decreasing function on R.
Show that decreases in the interval [0, ∞) and increases in the interval (-∞, 0].
Show that is neither increasing nor decreasing on R.
Without using the derivative, show that the function f(x) = | x | is
A. strictly increasing in (0, ∞)
B. strictly decreasing in (-∞, 0).
Without using the derivative show that the function f(x) = 7x - 3 is strictly increasing function on R.