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Thread: 3.2.15 mvt

  1. MHB Master
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    #1
    $\tiny{3.2.15}$
    Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. Graph the function the secant line through the endpoints, and the tangent line at $(c,f(c))$.
    $f(x)=\sqrt{x} \quad [0,4]$
    Are the secant line and the tangent line parallel?
    $\dfrac{{f(b)-f(a)}}{{b-a}}$
    then
    $f(0)=0 \quad f(4)=2 \quad m=\dfrac{1}{2}$
    then
    $f'(x)=\dfrac{1}{2\sqrt{x}}
    =\dfrac{1}{2}\quad\therefore \quad f'(1)=\dfrac{1}{2}$
    then
    $(c,f(c))=(1,1)$

    ok not sure if this is the de jour way but.......

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  3. MHB Master
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    #2
    Quote Originally Posted by karush View Post
    $\tiny{3.2.15}$
    Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. Graph the function the secant line through the endpoints, and the tangent line at $(c,f(c))$.
    $f(x)=\sqrt{x} \quad [0,4]$
    Are the secant line and the tangent line parallel?
    $\dfrac{{f(b)-f(a)}}{{b-a}}$
    then
    $f(0)=0 \quad f(4)=2 \quad m=\dfrac{1}{2}$
    then
    $f'(x)=\dfrac{1}{2\sqrt{x}}
    =\dfrac{1}{2}\quad\therefore \quad f'(1)=\dfrac{1}{2}$
    then
    $(c,f(c))=(1,1)$

    ok not sure if this is the de jour way but.......
    It's fine, well done.

  4. MHB Master
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    #3
    "De jour" way? Do you think the correct way to do a problem changes from day to day?

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    #4
    Quote Originally Posted by HallsofIvy View Post
    "De jour" way? Do you think the correct way to do a problem changes from day to day?
    I think the OP just means they are not sure if this is considered the most concise or elegant way, or if there are any steps that are not mathematically justified.

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