हिंदी

Show that the function given by f(x) = 3x + 17 is strictly increasing on R. - Mathematics

Advertisements
Advertisements

प्रश्न

Show that the function given by f(x) = 3x + 17 is strictly increasing on R.

योग

उत्तर

We have f(x) = 3x + 17

f(x) being a polynomial function, is continuous and derivable on R.

f'(x) `3 > 0, x in R`

⇒ f is strictly increasing on R.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Application of Derivatives - Exercise 6.2 [पृष्ठ २०५]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
अध्याय 6 Application of Derivatives
Exercise 6.2 | Q 2 | पृष्ठ २०५

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

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


Prove that the logarithmic function is strictly increasing on (0, ∞).


Water is dripping out from a conical funnel of semi-verticle angle `pi/4` at the uniform rate of `2 cm^2/sec`in the surface, through a tiny hole at the vertex of the bottom. When the slant height of the water level is 4 cm, find the rate of decrease of the slant height of the water.


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


Show that f(x) = \[\frac{1}{x}\] is a decreasing function on (0, ∞) ?


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


Find the interval in which the following function are increasing or decreasing f(x) = 8 + 36x + 3x2 − 2x?


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 − 5 ?


Find the interval in which the following function are increasing or decreasing  f(x) = 2x3 − 24x + 107  ?


Find the interval in which the following function are increasing or decreasing f(x) = x3 − 12x2 + 36x + 17 ?


Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{3}{10} x^4 - \frac{4}{5} x^3 - 3 x^2 + \frac{36}{5}x + 11\] ?


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


Show that the function f(x) = cot \[-\] l(sinx + cosx) is decreasing on \[\left( 0, \frac{\pi}{4} \right)\] and increasing on \[\left( 0, \frac{\pi}{4} \right)\] ?


Show that f(x) = (x − 1) ex + 1 is an increasing function for all x > 0 ?


Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?


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] ?


Show that f(x) = sin x − cos x is an increasing function on (−π/4, π/4) ?


Every invertible function is


Find the intervals in which the function \[f(x) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] is

(a) strictly increasing
(b) strictly decreasing


If x = cos2 θ and y = cot θ then find `dy/dx  at  θ=pi/4` 


Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q 


For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the value of x for which Total cost is decreasing.


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


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


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


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


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


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


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 ______


Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R


Show that f(x) = tan–1(sinx + cosx) is an increasing function in `(0, pi/4)`


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


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


The function f (x) = x2, for all real 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) = `x/(x^2 + 1)` is increasing function then the value of x lies in ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×