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

Find the intervals in which the function f given by f(x) = 2x³ − 3x² − 36x + 7 is

1. Strictly increasing
2. Strictly decreasing

Find the intervals in which the following functions are strictly increasing or decreasing:

x² + 2x − 5

Find the intervals in which the following functions are strictly increasing or decreasing:

10 − 6x − 2x²

Find the intervals in which the following functions are strictly increasing or decreasing:

−2x³ − 9x² − 12x + 1

Find the intervals in which the following functions are strictly increasing or decreasing:

 (x + 1)³ (x − 3)³

Find the intervals in which the following functions are strictly increasing or decreasing:

6 − 9x − x²

Show that y = `log(1+x) - (2x)/(2+x), x> -  1`, is an increasing function of x throughout its domain.

Find the values of x for  `y = [x(x - 2)]^2` is an increasing function.

Prove that  y = `(4sin theta)/(2 + cos theta) - theta` is an increasing function of θ in `[0, pi/2]`

Prove that the logarithmic function is strictly increasing on (0, ∞).

Prove that the function f given by f(x) = x² − x + 1 is neither strictly increasing nor strictly decreasing on (−1, 1).

Which of the following functions are strictly decreasing on `(0, pi/2)`?

1. cos x
2. cos 2x
3. cos 3x
4. tan x

On which of the following intervals is the function f given byf(x) = x¹⁰⁰ + sin x –1 strictly decreasing?

Find the least value of a such that the function f given by f (x) = x² + ax + 1 is strictly increasing on [1, 2].

Let I be any interval disjoint from (−1, 1). Prove that the function f given by `f(x) = x + 1/x` is strictly increasing on I.

Prove that the function f given by f(x) = log sin x is strictly increasing on `(0, pi/2)` and strictly decreasing on `(pi/2, pi)`

Prove that the function f given by f(x) = log cos x is strictly decreasing on `(0, pi/2)` and strictly increasing on `((3pi)/2, 2pi).`

Prove that the function given by f (x) = x³ – 3x² + 3x – 100 is increasing in R.

The interval in which y = x² e^–x is increasing is ______.

Find the intervals in which the function f given by `f(x) = (4sin x - 2x - x cos x)/(2 + cos x)` is (i) increasing (ii) decreasing.