Assertion (A): The function f(x) = x³ - 12x is strictly increasing in (-∞, -2) ∪ (2, ∞). Reason (R): For strictly increasing function f'(x) > 0.

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Question

Assertion-ReasonIncreasing Functions

Let f(x) be a continuous function on [a, b] and differentiable on (a, b). Then, this function f(x) is strictly increasing in (a, b) if

The function f(x) = x³ – 3x² + 12x – 18 is :

Increasing Functions

Decreasing Functions

Show that f(x) = eˣ – e⁻ˣ + x – tan⁻¹ x is strictly increasing in its domain.

Find the intervals in which the function f(x) = log x/x is strictly increasing or strictly decreasing.

Find the absolute maximum and absolute minimum values of the function f given by f(x) = x/2 + 2/x, on the interval [1, 2].

The function f(x) = kx – sin x is strictly increasing for