मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Show that function f(x) = tan x is increasing in π(0,π2).

Advertisements
Advertisements

प्रश्न

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

बेरीज
Advertisements

उत्तर

Given, f(x) = tan x

f'(x) = sec2x

But sec2x > 0, ∀x∈ (0, π/2)

Hence f(x) = tan x is strictly increasing in (0, π/2).

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2021-2022 (March) Set 1

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

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

  1. strictly increasing
  2. strictly decreasing

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

10 − 6x − 2x2


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


Show that f(x) = \[\frac{1}{1 + x^2}\] decreases in the interval [0, ∞) and increases in the interval (−∞, 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) = 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 − 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) = x4 − 4x ?


Show that f(x) = x − sin x is increasing for all x ∈ R ?


Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π) ?


Show that f(x) = tan x is an increasing function on (−π/2, π/2) ?


Prove that the following function is increasing on R f \[(x) =\]3 \[x^5\] + 40 \[x^3\] + 240\[x\] ?


Find the set of values of 'a' for which f(x) = x + cos x + ax + b is increasing on R ?


The function f(x) = 2 log (x − 2) − x2 + 4x + 1 increases on the interval


If the function f(x) = kx3 − 9x2 + 9x + 3 is monotonically increasing in every interval, then


If the function f(x) = x2 − kx + 5 is increasing on [2, 4], then


The radius r of a right circular cylinder is increasing uniformly at the rate of 0·3 cm/s and its height h is decreasing at the rate of 0·4 cm/s. When r = 3·5 cm and h = 7 cm, find the rate of change of the curved surface area of the cylinder. \[\left[ \text{ Use } \pi = \frac{22}{7} \right]\]


If the demand function is D = 50 - 3p - p2, find the elasticity of demand at (a) p = 5 (b) p = 2 ,  Interpret your result. 


Find the intervals in which the function `f("x") = (4sin"x")/(2+cos"x") -"x";0≤"x"≤2pi` is strictly increasing or strictly decreasing. 


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) = `x-(1)/x`, x ∈ R, x ≠ 0.


Choose the correct option from the given alternatives :

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


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 ______


State whether the following statement is True or False: 

The function f(x) = `3/x` + 10, x ≠ 0 is decreasing


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


The sides of a square are increasing at the rate of 0.2 cm/sec. When the side is 25cm long, its area is increasing at the rate of ______


Let the f : R → R be defined by f (x) = 2x + cosx, then f : ______.


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


The function f(x) = tanx – x ______.


The values of a for which the function f(x) = sinx – ax + b increases on R are ______.


The function f(x) = tan-1 (sin x + cos x) is an increasing function in:


The function f: N → N, where

f(n) = `{{:(1/2(n + 1), "If n is sold"),(1/2n, "if n is even"):}` is


Which of the following graph represent the strictly increasing function.


Let f: [0, 2]→R be a twice differentiable function such that f"(x) > 0, for all x ∈( 0, 2). If `phi` (x) = f(x) + f(2 – x), then `phi` is ______.


If f(x) = `x/(x^2 + 1)` is increasing function then the value of x lies in ______.


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


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


In which one of the following intervals is the function f(x) = x3 – 12x increasing?


For \[f(x)=x^3-3x^2+4x\], what is \[f'(x)\]?


For \[f(x)=4x^3-6x^2-72x+30\], which factorization of \[f'(x)\] is correct?


For \[f'(x)=12(x-3)(x+2)\], what are the critical points obtained from \[f'(x)=0\]?


For \[f'(x)=12(x-3)(x+2)\], what is the nature of \[f\] on \[(-2,3)\]?


Which statement about \[f'(x)=0\] and constant behaviour is correct?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×