हिंदी

Prove that the Following Functions Are Increasing on R F F ( X ) = 4 X 3 − 18 X 2 + 27 X − 27 ? - Mathematics

Advertisements
Advertisements

प्रश्न

Prove that the following function is increasing on R f \[f\left( x \right) = 4 x^3 - 18 x^2 + 27x - 27\] ?

योग
Advertisements

उत्तर

\[f\left( x \right) = 4 x^3 - 18 x^2 + 27x - 27\]

\[f'\left( x \right) = 12 x^2 - 36x + 27\]

\[ \Rightarrow f'\left( x \right) = 3\left( 4 x^2 - 12x + 9 \right)\]

\[ \Rightarrow f'\left( x \right) = 3 \left( 2x - 3 \right)^2 > 0, \forall x \in R\]

So, f(x) is increasing on R.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 17: Increasing and Decreasing Functions - Exercise 17.2 [पृष्ठ ३५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 17 Increasing and Decreasing Functions
Exercise 17.2 | Q 30.2 | पृष्ठ ३५

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 function f given by f(x) = log sin x is strictly increasing on `(0, pi/2)` and strictly decreasing on `(pi/2, pi)`


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 + 1  ?


Find the interval in which the following function are increasing or decreasing  f(x) = x4 − 4x3 + 4x2 + 15 ?


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


Show that f(x) = loga x, 0 < a < 1 is a decreasing function for all x > 0 ?


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


Find the interval in which f(x) is increasing or decreasing f(x) = sinx + |sin x|, 0 < x \[\leq 2\pi\] ?


Find the interval in which f(x) is increasing or decreasing f(x) = sinx(1 + cosx), 0 < x < \[\frac{\pi}{2}\] ?


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


State whether f(x) = tan x − x is increasing or decreasing its domain ?


Function f(x) = cos x − 2 λ x is monotonic decreasing when


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


The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.


The consumption expenditure Ec of a person with the income x. is given by Ec = 0.0006x2 + 0.003x. Find MPC, MPS, APC and APS when the income x = 200.


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


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) = 2 – 3x + 3x2 – x3, x ∈ R.


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 ______.


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

f(x) = 2x3 - 15x2 - 144x - 7 


State whether the following statement is True or False:

The function f(x) = `"x"*"e"^("x" (1 - "x"))` is increasing on `((-1)/2, 1)`.


Show that function f(x) =`3/"x" + 10`, x ≠ 0 is decreasing.


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


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


Find the values of x such that f(x) = 2x3 – 15x2 + 36x + 1 is increasing function


For every value of x, the function f(x) = `1/7^x` is ______ 


The function f(x) = tanx – x ______.


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) = x2 – 2x is increasing in the interval ____________.


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


Let `"f (x) = x – cos x, x" in "R"`, then f is ____________.


y = log x satisfies for x > 1, the inequality ______.


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×