HSC Arts (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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.

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

f(x) = 2x³ – 15x² – 84x – 7 

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

Prove that function f(x) = `x - 1/x`, x ∈ R and x ≠ 0 is increasing function

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

Show that the function f(x) = x³ + 10x + 7 for x ∈ R is strictly increasing

Test whether the function f(x) = x³ + 6x² + 12x − 5 is increasing or decreasing for all x ∈ R

Test whether the following function f(x) = 2 – 3x + 3x² – x³, x ∈ R is increasing or decreasing

Find the values of x for which the function f(x) = 2x³ – 6x² + 6x + 24 is strictly increasing

Find the values of x for which the function f(x) = x³ – 6x² – 36x + 7 is strictly increasing

Find the values of x, for which the function f(x) = x³ + 12x² + 36𝑥 + 6 is monotonically decreasing

Find the values of x for which f(x) = 2x³ – 15x² – 144x – 7 is

1. Strictly increasing
2. strictly decreasing

Show that function f(x) = tan x is increasing in `(0, π/2)`.

Lines `overliner = (hati + hatj - hatk) + λ(2hati - 2hatj + hatk)` and `overliner = (4hati - 3hatj + 2hatk) + μ(hati - 2hatj + 2hatk)` are coplanar. Find the equation of the plane determined by them.

Find the particular solution of the differential equation `dy/dx` = e^2y cos x, when x = `π/6`, y = 0

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

The function f(x) = sin⁴x + cos⁴x is an increasing function if ______.

Verify that y sec x = tan x + c is a solution of the differential equation `dy/dx + y tan x` = sec x.

Solution of differential equation `e^(x - 2y) = dy/dx` is ______.