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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

The amount of pollution content added in air in a city due to x-diesel vehicles is given by P(x) = 0.005x3 + 0.02x2 + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question.


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

  1. strictly increasing
  2. strictly decreasing

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


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).


Find the interval in which the following function are increasing or decreasing f(x) = 10 − 6x − 2x2  ?


Find the interval in which the following function are increasing or decreasing  f(x) = x2 + 2x − 5  ?


Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?


Show that f(x) = sin x is increasing on (0, π/2) and decreasing on (π/2, π) and neither increasing nor decreasing in (0, π) ?


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 the function f given by f(x) = 10x is increasing for all x ?


Show that f(x) = x + cos x − a is an increasing function on R for all values of a ?


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


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


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


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

 


The function \[f\left( x \right) = \frac{\lambda \sin x + 2 \cos x}{\sin x + \cos x}\] is increasing, if

 


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


 Prove that the function `f(x) = x^3- 6x^2 + 12x+5` is increasing on R. 


Find the values of x for which f(x) = `x/(x^2 + 1)` is (a) strictly increasing (b) decreasing.


Choose the correct alternative:

The function f(x) = x3 – 3x2 + 3x – 100, x ∈ R is


The function f(x) = x3 - 3x is ______.


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


Which of the following functions is decreasing on `(0, pi/2)`?


The function f (x) = 2 – 3 x is ____________.


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 ______.


Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly increasing in ______.


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


The function f(x) = xex(1 − x), x ∈ R, is ______.


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