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Choose the correct alternative: The number given by the Rolle’s theorem for the function x3 – 3x2, x ∈ [0, 3] is - Mathematics

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प्रश्न

Choose the correct alternative:

The number given by the Rolle’s theorem for the function x3 – 3x2, x ∈ [0, 3] is

पर्याय

  • 1

  • `sqrt(2)`

  • `3/2`

  • 2

MCQ

उत्तर

2

shaalaa.com
Mean Value Theorem
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Applications of Differential Calculus - Exercise 7.10 [पृष्ठ ५५]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 7 Applications of Differential Calculus
Exercise 7.10 | Q 12 | पृष्ठ ५५

संबंधित प्रश्‍न

Explain why Rolle’s theorem is not applicable to the following functions in the respective intervals

`f(x) = |1/x|, x ∈ [- 1, 1]`


Explain why Rolle’s theorem is not applicable to the following functions in the respective intervals

`f(x)` = tan x, x ∈ [0, π]


Explain why Rolle’s theorem is not applicable to the following functions in the respective intervals

`f(x)` = x – 2 log x, x ∈ [2, 7]


Using the Rolle’s theorem, determine the values of x at which the tangent is parallel to the x-axis for the following functions:

`f(x)` = x2 – x, x ∈ [0, 1]


Using the Rolle’s theorem, determine the values of x at which the tangent is parallel to the x-axis for the following functions:

`f(x) = (x^2 - 2x)/(x + 2), x ∈ [-1, 6]`


Using the Rolle’s theorem, determine the values of x at which the tangent is parallel to the x-axis for the following functions:

`f(x) = sqrt(x) - x/3, x ∈ [0, 9]`


Explain why Lagrange’s mean value theorem is not applicable to the following functions in the respective intervals:

`f(x) = (x + 1)/x, x ∈ [-1, 2]`


Using the Lagrange’s mean value theorem determine the values of x at which the tangent is parallel to the secant line at the end points of the given interval:

`f(x) = x^3 - 3x + 2, x ∈ [-2, 2]`


Show that the value in the conclusion of the mean value theorem for `f(x) = 1/x` on a closed interval of positive numbers [a, b] is `sqrt("ab")`


Show that the value in the conclusion of the mean value theorem for `f(x) = "A"x^2 + "B"x + "C"` on any interval [a, b] is `("a" + "b")/2`


A race car driver is kilometer stone 20. If his speed never exceeds 150 km/hr, what is the maximum kilometer he can reach in the next two hours


Suppose that for a function f(x), f'(x) ≤ 1 for all 1 ≤ x ≤ 4. Show that f(4) – f(1) ≤ 3


Show that there lies a point on the curve `f(x) = x(x + 3)e^(pi/2), -3 ≤ x ≤ 0` where tangent drawn is parallel to the x-axis


Using Mean Value Theorem prove that for, a > 0, b > 0, |e–a – eb| < |a – b|


Choose the correct alternative:

The number given by the Mean value theorem for the function `1/x`, x ∈ [1, 9] is


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