हिंदी

The maximum value of sinx + cosx is ______.

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प्रश्न

The maximum value of sinx + cosx is ______.

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उत्तर

The maximum value of sinx + cosx is `sqrt(2)`.

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

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 6 Application Of Derivatives
Solved Examples | Q 28 | पृष्ठ १३४

संबंधित प्रश्न

f (x) = [x] for −1 ≤ x ≤ 1, where [x] denotes the greatest integer not exceeding x Discuss the applicability of Rolle's theorem for the following function on the indicated intervals ?


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 ?


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) = x(x −2)2 on the interval [0, 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) = ex cos x on [−π/2, π/2] ?


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(x) = sin x + cos x on [0, π/2] ?


Verify Rolle's theorem for the following function on the indicated interval f(x) = 4sin x on [0, π] ?


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] ?


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 − 3x + 2 on [−1, 2] ?


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 theore f(x) = (x − 1)(x − 2)(x − 3) on [0, 4] ?


Show that the lagrange's mean value theorem is not applicable to the function
f(x) = \[\frac{1}{x}\] on [−1, 1] ?


Find a point on the parabola y = (x − 4)2, where the tangent is parallel to the chord joining (4, 0) and (5, 1) ?


Find a point on the curve y = x2 + x, where the tangent is parallel to the chord joining (0, 0) and (1, 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 < \[\frac{\pi}{2}\] ?


State Rolle's theorem ?


If the value of c prescribed in Rolle's theorem for the function f (x) = 2x (x − 3)n on the interval \[[0, 2\sqrt{3}] \text { is } \frac{3}{4},\] write the value of n (a positive integer) ?


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] ?


If the polynomial equation \[a_0 x^n + a_{n - 1} x^{n - 1} + a_{n - 2} x^{n - 2} + . . . + a_2 x^2 + a_1 x + a_0 = 0\] n positive integer, has two different real roots α and β, then between α and β, the equation \[n \ a_n x^{n - 1} + \left( n - 1 \right) a_{n - 1} x^{n - 2} + . . . + a_1 = 0 \text { has }\].

 


If 4a + 2b + c = 0, then the equation 3ax2 + 2bx + c = 0 has at least one real root lying in the interval


Rolle's theorem is applicable in case of ϕ (x) = asin x, a > a in


Find the maximum and minimum values of f(x) = secx + log cos2x, 0 < x < 2π


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


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


At what point, the slope of the curve y = – x3 + 3x2 + 9x – 27 is maximum? Also find the maximum slope.


The minimum value of `1/x log x` in the interval `[2, oo]` is


What does continuity on a closed interval guarantee?


For a continuous function on the closed interval \[a,d\], what does \[f(d)\] represent?


If a differentiable function has an absolute max or min at an interior point \[c\], what must be true?


Which points must always be checked when finding absolute extrema on a closed interval \[a,b\]?


How are the absolute maximum and absolute minimum determined after evaluating \[f(x)\] at all critical points and endpoints?


What is \[f(0)\] for \[f(x)=12x^{\frac{4}{3}}-6x^{\frac{1}{3}}\]?


What are the absolute extrema of \[f(x)=12x^{\frac{4}{3}}-6x^{\frac{1}{3}}\] on \[-1,1\]?


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