Question

The interval in which the Lagrange's theorem is applicable for the function f(x)=1/x is
Options
O [-3.3]
[-2.2]
(2.3]
(-1.1]​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The interval in which the Lagrange's theorem is applicable for the function f(x)=1/x is

• [-3, 3]

• [-2, 2]

• (2, 3]

• (-1, 1]

CONCEPT TO BE IMPLEMENTED

LAGRANGE'S MEAN VALUE THEOREM

If (i) f(x) is continuous in the closed interval [a, b] and

(ii) f'(x) exists in the open interval (a, b)

Then there exists at least one value of x say c in (a, b) such that

$\sf{f(b) - f(a) = f'(c) (b-a) }$

EVALUATION

Here the given function is

$\displaystyle \sf{f(x) = \frac{1}{x} }$

Clearly the denominator vanishes at x = 0

So the given function f(x) is continuous and differentiable everywhere except x = 0

So the function f(x) is continuous and differentiable in the interval containing the point x = 0

Since [-3, 3] contains the point 0

So in this interval Lagrange's theorem is not applicable for the function f(x)

Since [-3, 2] contains the point 0

So in this interval Lagrange's theorem is not applicable for the function f(x)

Since (2, 3] does not contain the point 0

So in this interval Lagrange's theorem is applicable for the function f(x)

Since (-1, 1] contains the point 0

So in this interval Lagrange's theorem is not applicable for the function f(x)

FINAL ANSWER

The interval in which the Lagrange's theorem is applicable for the function is (2, 3]

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