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Minimum value of f if f(x) = sinx in [-π2,π2] is ______. - Mathematics

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प्रश्न

Minimum value of f if f(x) = sinx in `[(-pi)/2, pi/2]` is ______.

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उत्तर

Minimum value of f if f(x) = sinx in `[(-pi)/2, pi/2]` is –1.

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अध्याय 6: Application Of Derivatives - Solved Examples [पृष्ठ १३४]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 6 Application Of Derivatives
Solved Examples | Q 27 | पृष्ठ १३४

संबंधित प्रश्न

f(x) = 3 + (x − 2)2/3 on [1, 3] Discuss the applicability of Rolle's theorem for the following function on the indicated intervals ? 


f (x) = 2x2 − 5x + 3 on [1, 3] Discuss the applicability of Rolle's theorem for the following function on the indicated intervals ?


\[f\left( x \right) = \begin{cases}- 4x + 5, & 0 \leq x \leq 1 \\ 2x - 3, & 1 < x \leq 2\end{cases}\] Discuss the applicability of Rolle's theorem for the following function on the indicated intervals ?


Verify Rolle's theorem for the following function on the indicated interval f(x) = x2 − 4x + 3 on [1, 3] ?


Verify Rolle's theorem for the following function on the indicated interval  f(x) = sin 2x on [0, π/2] ?


Verify Rolle's theorem for the following function on the indicated interval f(x) = ex sin x on [0, π] ?


Verify Rolle's theorem for the following function on the indicated interval f(x) = ecos x on [−π/2, π/2] ?


Verify Rolle's theorem for the following function on the indicated interval f (x) = \[\frac{\sin x}{e^x}\] on 0 ≤ x ≤ π ?


Verify Rolle's theorem for the following function on the indicated interval \[f\left( x \right) = \frac{x}{2} - \sin\frac{\pi x}{6} \text { on }[ - 1, 0]\]?


Verify Rolle's theorem for the following function on the indicated interval f(x) = sin4 x + cos4 x on \[\left[ 0, \frac{\pi}{2} \right]\] ?


At what point  on the following curve, is the tangent parallel to x-axis y = x2 on [−2, 2]
?


At what point  on the following curve, is the tangent parallel to x-axis y = \[e^{1 - x^2}\] on [−1, 1] ?


At what point  on the following curve, is the tangent parallel to x-axis y = 12 (x + 1) (x − 2) on [−1, 2] ?


If f : [−5, 5] → is differentiable and if f' (x) doesnot vanish anywhere, then prove that f (−5) ± f (5) ?


It is given that the Rolle's theorem holds for the function f(x) = x3 + bx2 + cx, x  \[\in\] at the point x = \[\frac{4}{3}\] , Find the values of b and c ?


Examine if Rolle's theorem is applicable to any one of the following functions.
(i) f (x) = [x] for x ∈ [5, 9]
(ii) f (x) = [x] for x ∈ [−2, 2]
Can you say something about the converse of Rolle's Theorem from these functions?


Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem f(x) = x2 − 1 on [2, 3] ?


Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem  f(x) = x2 − 2x + 4 on [1, 5] ?


Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem f(x) = 2x − x2 on [0, 1] ?


Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theore \[f\left( x \right) = \sqrt{25 - x^2}\] on [−3, 4] ?


Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem \[f\left( x \right) = x + \frac{1}{x} \text { on }[1, 3]\] ?


Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem \[f\left( x \right) = \sqrt{x^2 - 4} \text { on }[2, 4]\] ?


Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem  f(x) = x2 + x − 1 on [0, 4] ?


Verify the  hypothesis and conclusion of Lagrange's man value theorem for the function
f(x) = \[\frac{1}{4x - 1},\] 1≤ x ≤ 4 ?

 


Find a point on the curve y = x2 + x, where the tangent is parallel to the chord joining (0, 0) and (1, 2) ?


Find the points on the curve y = x3 − 3x, where the tangent to the curve is parallel to the chord joining (1, −2) and (2, 2) ?


If f (x) = Ax2 + Bx + C is such that f (a) = f (b), then write the value of c in Rolle's theorem ? 


State Rolle's theorem ?


The value of c in Rolle's theorem when
f (x) = 2x3 − 5x2 − 4x + 3, x ∈ [1/3, 3] is

 


The value of c in Lagrange's mean value theorem for the function f (x) = x (x − 2) when x ∈ [1, 2] is


Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi-vertical angle α is one-third that of the cone and the greatest volume of the cylinder is `(4)/(27) pi"h"^3 tan^2 α`.


Find the difference between the greatest and least values of the function f(x) = sin2x – x, on `[- pi/2, pi/2]`


If the graph of a differentiable function y = f (x) meets the lines y = – 1 and y = 1, then the graph ____________.


If f(x) = ax2 + 6x + 5 attains its maximum value at x = 1, then the value of a is


The function f(x) = [x], where [x] =greater integer of x, is


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