मराठी

Determine Whether F(X) = −X/2 + Sin X is Increasing Or Decreasing on (−π/3, π/3) ? - Mathematics

Advertisements
Advertisements

प्रश्न

Determine whether f(x) = −x/2 + sin x is increasing or decreasing on (−π/3, π/3) ?

बेरीज

उत्तर

f(x)=x2+sinx

f(x)=12+cosx

 Here, 

π3<x<π3

cosx>12

12+cosx>0

f(x)>0,x(π3,π3)

So,f (x) is increasing on (π3,π3).

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Increasing and Decreasing Functions - Exercise 17.2 [पृष्ठ ३५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 17 Increasing and Decreasing Functions
Exercise 17.2 | Q 25 | पृष्ठ ३५

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 function f given by f(x) = 2x3 − 3x2 − 36x + 7 is

  1. Strictly increasing
  2. Strictly decreasing

Prove that the function f given by f(x) = log cos x is strictly decreasing on (0,π2) and strictly increasing on (3π2,2π).


Let f be a function defined on [a, b] such that f '(x) > 0, for all x ∈ (a, b). Then prove that f is an increasing function on (a, b).


Prove that f(x) = ax + b, where a, b are constants and a > 0 is an increasing function on R ?


Without using the derivative, show that the function f (x) = | x | is.
(a) strictly increasing in (0, ∞)
(b) strictly decreasing in (−∞, 0) .


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) =  5x323x52  x > 0 ?


Show that f(x) = x3 − 15x2 + 75x − 50 is an increasing function for all x ∈ R ?


Show that the function f(x) = cot l(sinx + cosx) is decreasing on (0,π4) and increasing on (0,π4) ?


State when a function f(x) is said to be increasing on an interval [a, b]. Test whether the function f(x) = x2 − 6x + 3 is increasing on the interval [4, 6] ?


Let f defined on [0, 1] be twice differentiable such that | f (x) | ≤ 1 for all x ∈ [0, 1]. If f(0) = f(1), then show that | f'(x) | < 1 for all x ∈ [ 0, 1] ?


If g (x) is a decreasing function on R and f(x) = tan−1 [g (x)]. State whether f(x) is increasing or decreasing on R ?


Write the set of values of a for which the function f(x) = ax + b is decreasing for all x ∈ R ?


Write the interval in which f(x) = sin x + cos x, x ∈ [0, π/2] is increasing ?


Write the set of values of a for which f(x) = cos x + a2 x + b is strictly increasing on R ?


The interval of increase of the function f(x) = x − ex + tan (2π/7) is


The function f(x)=loge(x3+x6+1) is of the following types:


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


Function f(x) = loga x is increasing on R, if


The function f(x) = x9 + 3x7 + 64 is increasing on


The edge of a cube is decreasing at the rate of0.6cmsec. Find the rate at which its volume is decreasing, when the edge of the cube is 2 cm.


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

f(x) = x2 + 2x - 5 


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


By completing the following activity, find the values of x such that f(x) = 2x3 – 15x2 – 84x – 7 is decreasing function.

Solution: f(x) = 2x3 – 15x2 – 84x – 7

∴ f'(x) =

∴ f'(x) = 6()()

Since f(x) is decreasing function.

∴ f'(x) < 0

Case 1: () > 0 and (x + 2) < 0

∴ x ∈

Case 2: () < 0 and (x + 2) > 0

∴ x ∈

∴ f(x) is decreasing function if and only if x ∈


The function f(x) = 9 - x5 - x7 is decreasing for


f(x) = {0,         x=0x-3,  x>0 The function f(x) is ______


In which interval is the given function, f(x) = 2x3 - 21x2 + 72x + 19 monotonically decreasing?


The values of k for which the function f(x) = kx3 – 6x2 + 12x + 11 may be increasing on R are ______.


y = x(x – 3)2 decreases for the values of x given by : ______.


In case of decreasing functions, slope of tangent and hence derivative is ____________.


The function f (x) = x2, for all real x, is ____________.


Let f (x) = x – cos x, xR, then f is ____________.


In (0,π2),  the function f (x) = xsin x is ____________.


State whether the following statement is true or false.

If f'(x) > 0 for all x ∈ (a, b) then f(x) is decreasing function in the interval (a, b).


Let f(x) be a function such that; f'(x) = log1/3(log3(sinx + a)) (where a ∈ R). If f(x) is decreasing for all real values of x then the exhaustive solution set of a is ______.


If f(x) = x5 – 20x3 + 240x, then f(x) satisfies ______.


The interval in which the function f(x) = 4x2+1x is decreasing is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×
Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.