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

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

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प्रश्न

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

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उत्तर

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

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पाठ 1.4: Applications of Derivatives - Q.2

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Price P for demand D is given as P = 183 +120D - 3D2 Find D for which the price is increasing


Show that the function `f(x) = x^3 - 3x^2 + 6x - 100` is increasing on R


Find the intervals in which the function f given by f(x) = 2x3 − 3x2 − 36x + 7 is

  1. Strictly increasing
  2. Strictly decreasing

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

x2 + 2x − 5


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


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.


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


Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 15x2 + 36x + 1 ?


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 + 7 ?


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


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


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


The function f(x) = cot−1 x + x increases in the interval


f(x) = 2x − tan−1 x − log \[\left\{ x + \sqrt{x^2 + 1} \right\}\] is monotonically increasing when

 


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


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).


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.


Test whether the following functions are increasing or decreasing : f(x) = x3 – 6x2 + 12x – 16, x ∈ R.


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


State whether the following statement is True or False: 

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


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


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) = `|x - 1|/x^2` is monotonically decreasing on ______.


Function f(x) = `log(1 + x) - (2x)/(2 + x)` is monotonically increasing when ______.


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))` = ______.


The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.


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