मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

State whether the following statement is True or False: If the function f(x) = x2 + 2x – 5 is an increasing function, then x < – 1 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

State whether the following statement is True or False: 

If the function f(x) = x2 + 2x – 5 is an increasing function, then x < – 1

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

उत्तर

False 

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.4: Applications of Derivatives - Q.3

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Find the intervals in which f(x) = sin 3x – cos 3x, 0 < x < π, is strictly increasing or strictly decreasing.


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


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


Prove that the function f(x) = loge x is increasing on (0, ∞) ?


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


Find the interval in which the following function are increasing or decreasing f(x) = 6 + 12x + 3x2 − 2x3 ?


Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] ?


Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \log\left( 2 + x \right) - \frac{2x}{2 + x}, x \in R\] ?


Determine the values of x for which the function f(x) = x2 − 6x + 9 is increasing or decreasing. Also, find the coordinates of the point on the curve y = x2 − 6x + 9 where the normal is parallel to the line y = x + 5 ? 


Show that f(x) = e2x is increasing on R.


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


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−1 (sin x + cos x) is a decreasing function on the interval (π/4, π/2) ?


Write the set of values of 'a' for which f(x) = loga x is decreasing in its domain ?


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


The function \[f\left( x \right) = \log_e \left( x^3 + \sqrt{x^6 + 1} \right)\] is of the following types:


If the function f(x) = cos |x| − 2ax + b increases along the entire number scale, then

 


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


The total cost of manufacturing x articles is C = 47x + 300x2 − x4.  Find x, for which average cost is increasing.


Find MPC ( Marginal propensity to Consume ) and APC ( Average Propensity to Consume ) if the expenditure Ec of a person with income I is given as Ec = ( 0.0003 ) I2 + ( 0.075 ) I when I = 1000.


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


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


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 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 


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


The slope of tangent at any point (a, b) is also called as ______.


The total cost function for production of articles is given as C = 100 + 600x – 3x2, then the values of x for which the total cost is decreasing is  ______


If f(x) = [x], where [x] is the greatest integer not greater than x, then f'(1') = ______.


A ladder 20 ft Jong leans against a vertical wall. The top-end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall is ______ 


The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval ______.


Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f '(x) = 0 for every x, then ____________.


The function f(x) = mx + c where m, c are constants, is a strict decreasing function for all `"x" in "R"` , if ____________.


The function f(x) = tan-1 x is ____________.


The function `"f"("x") = "x"/"logx"` increases on the interval


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 ______.


Let f : R `rightarrow` R be a positive increasing function with `lim_(x rightarrow ∞) (f(3x))/(f(x))` = 1 then `lim_(x rightarrow ∞) (f(2x))/(f(x))` = ______.


A function f is said to be increasing at a point c if ______.


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?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×