Assertion (A) : f(x) = e^(–x) is a decreasing function, where x ∈ ℝ. Reason (R) : If f'(x) < 0, then f(x) is a decreasing function.

Free previous-year papers & practice for JEE, NEET and CBSE Boards.

Free previous-year papers & practice for JEE, NEET and CBSE Boards.

Decreasing Functions and Their Properties, First Derivative Test for Increasing and Decreasing Functions | PadhAiPro

Question

Assertion-ReasonDecreasing Functions and Their PropertiesFirst Derivative Test for Increasing and Decreasing 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 and Their Properties

Decreasing Functions and Their Properties

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].

Find the interval in which the function f(x) = x⁴ – 4x³ + 10 is strictly decreasing.