Question

Examine whether the function f(x)=x²-6x +1 in [1,3] satisfies the hypothesis of
Lagrange's Mean value Theorem Hence find the coordinate of the point at which the
tangent is parallel to the chord joining the points(1,-4) and (3,-8)
​

Answer 1

The coordinate of the point is (2,-7)

Step-by-step explanation:

Given function f(x)=x²-6x +1 in [1,3]

According to Lagrange's mean value theorem-

1. given function should be continuous and this given function is polynomial , so it is continuous for all real values, so in the domain [1,3] also.

2.  given function should be differential. because it is polynomial its differentiation is possible in any given domain, so in the given domain (1,3) also.

so given function satisfies this theorem.

then there exists a point c in (1,3) such that

$\frac{-8-(-4)}{3-1}= f'(c)$= 2*c-6

2*c - 6 = -2

c = 2

so x=2

putting this value in given equation

y=$2^{2} - 6*2 +1$

y= -7

so at point (2,-7) the  tangent is parallel to the chord joining the points(1,-4) and (3,-8) .

Know more

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