Question

The geometrical meaning of L.M.V.T. is that the
tangent at c€(a,b) is ----​

Answer 1

SOLUTION

TO DETERMINE

The geometrical meaning of L.M.V.T. is that the tangent at c ∈ (a,b) is

EVALUATION

Full form of L.M.V.T is Lagrange's Mean Value Theorem

Lagrange's Mean Value Theorem states that

If a function f is defined on the closed interval [a,b] such that

i) f is continuous on the closed interval [a, b]

ii) f is differentiable on the open interval (a, b)

Then there exists a value of x say c ∈ (a,b) such that

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

Let A and B be the points on the curve y = f(x) corresponding to x = a and x = b

Then slope of chord AB

$\displaystyle\sf{= \frac{f(b) - f(a)}{b - a} }$

Again slope of chord AB = f'(c)

$\displaystyle\sf{ \therefore \: f'(c) = \frac{f(b) - f(a)}{b - a} }$

Hence the Lagrange's Mean Value Theorem asserts that if a curve AB has a tangent at each of its points then there exists at least one point C on this curve , the tangent at which is parallel to the chord AB

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Answer 2

Answer:

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