मराठी

The value of c in Mean value theorem for the function f(x) = x(x – 2), x ∈ [1, 2] is ______. - Mathematics

Advertisements
Advertisements

प्रश्न

The value of c in Mean value theorem for the function f(x) = x(x – 2), x ∈ [1, 2] is ______.

पर्याय

  • `3/2`

  • `2/3`

  • `1/2`

  • `3/2`

MCQ
रिकाम्या जागा भरा

उत्तर

The value of c in Mean value theorem for the function f(x) = x(x – 2), x ∈ [1, 2] is `3/2`.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Continuity And Differentiability - Solved Examples [पृष्ठ १०५]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 5 Continuity And Differentiability
Solved Examples | Q 35 | पृष्ठ १०५

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Verify Lagrange’s mean value theorem for the function f(x)=x+1/x, x ∈ [1, 3]


Check whether the conditions of Rolle’s theorem are satisfied by the function
f (x) = (x - 1) (x - 2) (x - 3), x ∈ [1, 3]


Examine if Rolle’s Theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s Theorem from these examples?

f (x) = [x] for x ∈ [5, 9]


Examine if Rolle’s Theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s Theorem from these examples?

f (x) = x2 – 1 for x ∈ [1, 2]


Examine the applicability of Mean Value Theorem for all three functions given in the above exercise 2. 


Verify Lagrange's Mean Value Theorem for the following function:

`f(x ) = 2 sin x +  sin 2x " on " [0, pi]`


Verify the Lagrange’s mean value theorem for the function: 
`f(x)=x + 1/x ` in the interval [1, 3]


Verify Langrange’s mean value theorem for the function:

f(x) = x (1 – log x) and find the value of  c in the interval [1, 2].


Verify Mean value theorem for the function f(x) = 2sin x + sin 2x on [0, π].


f(x) = x(x – 1)2 in [0, 1]


f(x) = log(x2 + 2) – log3 in [–1, 1]


f(x) = `sqrt(4 - x^2)` in [– 2, 2]


Find the points on the curve y = (cosx – 1) in [0, 2π], where the tangent is parallel to x-axis


Using Rolle’s theorem, find the point on the curve y = x(x – 4), x ∈ [0, 4], where the tangent is parallel to x-axis


f(x) = `1/(4x - 1)` in [1, 4]


f(x) = x3 – 2x2 – x + 3 in [0, 1]


f(x) = sinx – sin2x in [0, π]


Find a point on the curve y = (x – 3)2, where the tangent is parallel to the chord joining the points (3, 0) and (4, 1)


The value of c in Rolle’s theorem for the function f(x) = x3 – 3x in the interval `[0, sqrt(3)]` is ______.


Rolle’s theorem is applicable for the function f(x) = |x – 1| in [0, 2].


If x2 + y2 = 1, then ____________.


A value of c for which the Mean value theorem holds for the function f(x) = logex on the interval [1, 3] is ____________.


If `1/(a + ω) + 1/(b + ω) + 1/(c + ω) + 1/(d + ω) = 1/ω`, where a, b, c, d ∈ R and ω is a cube root of unity then `sum 3/(a^2 - a + 1)` is equal to


Rolle's Theorem holds for the function x3 + bx2 + cx, 1 ≤ x ≤ 2 at the point `4/3`, the value of b and c are


P(x) be a polynomial satisfying P(x) – 2P'(x) = 3x3 – 27x2 + 38x + 1.

If function

f(x) = `{{:((P^n(x) + 18)/6, x ≠ π/2),(sin^-1(ab) + cos^-1(a + b - 3ab), x = π/2):}`

is continuous at x = ` π/2`, then (a + b) is equal to ______.


`lim_(x→0) sqrt(1 - cosx)/(sqrt(2)x)` is ______.


Let f(1) = –2 and f'(x) ≥ 4.2 for 1 ≤ x ≤ 6. The possible value of f(6) lies in the interval ______. 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×