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

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 ?

Find the interval in which the following function are increasing or decreasing f(x) = 6 + 12x + 3x² − 2x³ ?

Find the interval in which the following function are increasing or decreasing  f(x) = 2x³ − 24x + 107  ?

Find the interval in which the following function are increasing or decreasing f(x) = −2x³ − 9x² − 12x + 1  ?

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

Find the interval in which the following function are increasing or decreasing f(x) = x³ − 12x² + 36x + 17 ?

Find the interval in which the following function are increasing or decreasing  f(x) = 2x³ − 24x + 7 ?

Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{3}{10} x^4 - \frac{4}{5} x^3 - 3 x^2 + \frac{36}{5}x + 11\] ?