हिंदी

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

Advertisements
Advertisements

प्रश्न

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

रिक्त स्थान भरें

उत्तर

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

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Application Of Derivatives - Solved Examples [पृष्ठ १३४]

APPEARS IN

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

संबंधित प्रश्न

f (x) = sin \[\frac{1}{x}\] for −1 ≤ x ≤ 1 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) = x(x − 1)2 on [0, 1] ?


Verify Rolle's theorem for the following function on the indicated interval  f (x) = (x2 − 1) (x − 2) on [−1, 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(x) = sin 3x on [0, π] ?


Verify Rolle's theorem for the following function on the indicated interval f (x) = \[{e^{1 - x}}^2\] on [−1, 1] ?


Verify Rolle's theorem for the following function on the indicated interval \[f\left( x \right) = \frac{6x}{\pi} - 4 \sin^2 x \text { on } [0, \pi/6]\] ?


Verify Rolle's theorem for the following function on the indicated interval f(x) = x2 − 5x + 4 on [1, 4] ?


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


Using Rolle's theorem, find points on the curve y = 16 − x2x ∈ [−1, 1], where tangent is parallel to x-axis.


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) ?


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) = x3 − 2x2 − x + 3 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 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(x) = x(x + 4)2 on [0, 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] ?


Discuss the applicability of Lagrange's mean value theorem for the function
f(x) = | x | on [−1, 1] ?


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

 


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) ?


Using Lagrange's mean value theorem, prove that (b − a) sec2 a < tan b − tan a < (b − a) sec2 b
where 0 < a < b < \[\frac{\pi}{2}\] ?


Find the value of c prescribed by Lagrange's mean value theorem for the function \[f\left( x \right) = \sqrt{x^2 - 4}\] defined on [2, 3] ?


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 Rolle's theorem for the function \[f\left( x \right) = \frac{x\left( x + 1 \right)}{e^x}\] defined on [−1, 0] is


The value of c in Rolle's theorem for the function f (x) = x3 − 3x in the interval [0,\[\sqrt{3}\]] is 

 


If f (x) = ex sin x in [0, π], then c in Rolle's theorem is



Find the area of greatest rectangle that can be inscribed in an ellipse `x^2/"a"^2 + y^2/"b"^2` = 1


The least value of the function f(x) = 2 cos x + x in the closed interval `[0, π/2]` is:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×