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Lagrange's mean value theorem is , f(b...

Lagrange's mean value theorem is ,
`f(b)-f(a)=(b-a)f'(c ), a lt c lt b`
if `f(x)=sqrt(x)` and a=4, b=9, find c.

Text Solution

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The correct Answer is:
c=6.25
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Knowledge Check

  • In the mean value theorem f(b)-f(a)=(b-a)f'(c )(a lt c lt b) , if a=4, b=9 and f(x)=sqrt(x) , then the value of c is -

    A
    8
    B
    5.25
    C
    4
    D
    6.25

  • If from Lagrange's Mean Value theorem we have, f(4)-f(1)=(4-1)f'(c ) then -

    A
    `1le c le 4`
    B
    `0 le c lt 4`
    C
    `1 lt c le 4`
    D
    `1lt c lt 4 `

  • In the mean value theorem f(b)-f(a)=(b-a)f'(c )(a lt c lt b), "if " a=(pi)/(6), b=(5pi)/(6) and f(x) =log(sinx) , then the value of c is -

    A
    `(pi)/(4)`
    B
    `(pi)/(3)`
    C
    `(pi)/(2)`
    D
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    Using Largrange's mean value theorem f(b)-f(a)=(b-a)f'(c ) find the value of c, given f(x)=x(x-1)(x-2), a=0 and b=(1)/(2) .

    In the following Lagrange's mean value theorem, f(a+h)-f(a)=hf'(a+theta h), 0 lt theta lt 1 If f(x)=(1)/(3) x^(3)-(3)/(2) x^(2)+2x, a=0 and h=3 " find " theta .

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    Using Lagrange's mean value theorem show that, (b-a)/(b) lt "log"(b)/(a) lt (b-a)/(a) , where 0 lt a lt b .

    In the mean value theorem f(a+h)=f(a)+hf'(a+theta h) ( 0 lt theta lt 1) , if f(x)=sqrt(x), a=1, h=3 , then the value of theta is -

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