HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Test whether the following functions are increasing or decreasing : f(x) = x³ – 6x² + 12x – 16, x ∈ R.

Test whether the following functions are increasing or decreasing : f(x) = 2 – 3x + 3x² – x³, x ∈ R.

Test whether the following functions are increasing or decreasing: f(x) = `x-(1)/x`, x ∈ R, x ≠ 0.

Find the values of x for which the following functions are strictly increasing : f(x) = 2x³ – 3x² – 12x + 6

Find the values of x for which the following functions are strictly increasing:

f(x) = 3 + 3x – 3x² + x³

Find the values of x for which the following func- tions are strictly increasing : f(x) = x³ – 6x² – 36x + 7

Find the values of x for which the following functions are strictly decreasing:

f(x) = 2x³ – 3x² – 12x + 6

Find the values of x for which the following functions are strictly decreasing : f(x) = `x + (25)/x`

Find the values of x for which the following functions are strictly decreasing : f(x) = x³ – 9x² + 24x + 12

Find the values of x for which the function f(x) = x³ – 12x² – 144x + 13 (a) increasing (b) decreasing

Find the values of x for which f(x) = `x/(x^2 + 1)` is (a) strictly increasing (b) decreasing.

show that f(x) = `3x + (1)/(3x)` is increasing in `(1/3, 1)` and decreasing in `(1/9, 1/3)`.

Show that f(x) = x – cos x is increasing for all x.

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

Prove that y = `(4sinθ)/(2 + cosθ) - θ` is an increasing function if `θ ∈[0, pi/2]`

Choose the correct option from the given alternatives :

Let f(x) = x³ – 6x² + 9x + 18, then f(x) is strictly decreasing in ______.

Solve the following : Find the intervals on which the function y = x^x, (x > 0) is increasing and decreasing.

Solve the following:

Find the intervals on which the function f(x) = `x/logx` is increasing and decreasing.

Use quantifiers to convert the following open sentences defined on N, into a true statement.

n² ≥ 1

Find the value of x, such that f(x) is decreasing function.

f(x) = 2x³ – 15x² – 84x – 7