Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Prove that the function f(x) = log_a x is increasing on (0, ∞) if a > 1 and decreasing on (0, ∞), if 0 < a < 1 ?

Show that f(x) = \[\frac{1}{x}\] is a decreasing function on (0, ∞) ?

Show that f(x) = \[\frac{1}{1 + x^2}\] decreases in the interval [0, ∞) and increases in the interval (−∞, 0] ?

Show that f(x) = \[\frac{1}{1 + x^2}\] 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 ?

Find the interval in which the following function are increasing or decreasing f(x) = 10 − 6x − 2x²  ?

Find the interval in which the following function are increasing or decreasing  f(x) = x² + 2x − 5  ?

Find the interval in which the following function are increasing or decreasing  f(x) = 6 − 9x − x²  ?

Find the interval in which the following function are increasing or decreasing   f(x) = 2x³ − 12x² + 18x + 15 ?

Find the interval in which the following function are increasing or decreasing f(x) = 5 + 36x + 3x² − 2x³ ?

Find the interval in which the following function are increasing or decreasing f(x) = 8 + 36x + 3x² − 2x³ ?

Find the interval in which the following function are increasing or decreasing  f(x) = 5x³ − 15x² − 120x + 3 ?

Find the interval in which the following function are increasing or decreasing f(x) = x³ − 6x² − 36x + 2 ?

Find the interval in which the following function are increasing or decreasing f(x) = 2x³ − 15x² + 36x + 1 ?

Find the interval in which the following function are increasing or decreasing f(x) = 2x³ + 9x² + 12x + 20  ?

Find the interval in which the following function are increasing or decreasing f(x) = 2x³ − 9x² + 12x − 5 ?