Advertisements
Advertisements
प्रश्न
Show that the lagrange's mean value theorem is not applicable to the function
f(x) = \[\frac{1}{x}\] on [−1, 1] ?
Advertisements
उत्तर
Given:
Clearly, \[f\left( x \right)\] does not exist for x = 0
Thus, the given function is discontinuous on \[\left[ - 1, 1 \right]\] .
Hence, Lagrange's mean value theorem is not applicable for the given function on \[\left[ - 1, 1 \right]\]
APPEARS IN
संबंधित प्रश्न
\[f\left( x \right) = \begin{cases}- 4x + 5, & 0 \leq x \leq 1 \\ 2x - 3, & 1 < x \leq 2\end{cases}\] 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 − 8x + 12 on [2, 6] ?
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) = (x − 1) (x − 2)2 on [1, 2] ?
Verify Rolle's theorem for the following function on the indicated interval f (x) = x2 + 5x + 6 on the interval [−3, −2] ?
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 \[f\left( x \right) = \frac{6x}{\pi} - 4 \sin^2 x \text { on } [0, \pi/6]\] ?
Verify Rolle's theorem for the following function on the indicated interval f(x) = x2 − 5x + 4 on [1, 4] ?
Using Rolle's theorem, find points on the curve y = 16 − x2, x ∈ [−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] ?
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] ?
State Rolle's theorem ?
For the function f (x) = x + \[\frac{1}{x}\] ∈ [1, 3], the value of c for the Lagrange's mean value theorem is
Rolle's theorem is applicable in case of ϕ (x) = asin x, a > a in
The value of c in Lagrange's mean value theorem for the function f (x) = x (x − 2) when x ∈ [1, 2] is
Find the points on the curve x2 + y2 − 2x − 3 = 0 at which the tangents are parallel to the x-axis ?
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]`
Minimum value of f if f(x) = sinx in `[(-pi)/2, pi/2]` is ______.
The maximum value of sinx + cosx is ______.
At x = `(5pi)/6`, f(x) = 2 sin3x + 3 cos3x is ______.
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 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 \[f(a)\] represent?
For a continuous function on the closed interval \[a,d\], what does \[f(b)\] represent?
For a continuous function on the closed interval \[a,d\], what does \[f(d)\] represent?
Which statement about local extrema and absolute extrema is correct?
Which points are critical points for a function \[f\]?
How are the absolute maximum and absolute minimum determined after evaluating \[f(x)\] at all critical points and endpoints?
For \[f(x)=12x^{\frac{4}{3}}-6x^{\frac{1}{3}}\], which derivative is correct?
What is \[f(0)\] for \[f(x)=12x^{\frac{4}{3}}-6x^{\frac{1}{3}}\]?
