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Math Help - Rolles Theorem

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    Rolles Theorem

    Determine if the Rolles theorem can be applied. If it applies find "c" such that f(x)=(x-2)(x+3)^2, [-3,2]
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    Quote Originally Posted by sderosa518 View Post
    Determine if the Rolles theorem can be applied. If it applies find "c" such that f(x)=(x-2)(x+3)^2, [-3,2]
    f is differentiable and continuous since its a polynomial function
    and f(-3)=f(2)
    so the rolle's theorem can be applied here

    I do not know what do you mean with:

    Quote Originally Posted by sderosa518 View Post
    find "c" such that f(x)=(x-2)(x+3)^2, [-3,2]
    I think you mean find "c" that satisfies the rolle's theorem, right?
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    Yes!!!
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    Quote Originally Posted by sderosa518 View Post
    Yes!!!
    you want to solve f'(c)=0 for c ..
    so ?
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    This is what I got. I use the product rule to solve.

    3x^2+8x-3

    Not sure if I am right or not
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    Quote Originally Posted by sderosa518 View Post
    This is what I got. I use the product rule to solve.

    3x^2+8x-3

    Not sure if I am right or not
    correct
    so f'(x)=3x^2+8x-3
    hence f'(c)=3c^2+8c-3
    f'(c)=0 \rightarrow 3c^2+8c-3=0
    now solve the last equation for c
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    Any hint on how to solve it?

    Should I factor a 3 out or factoriztion (x-1)(x+1)
    or just simply solve for zero
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  8. #8
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    Quote Originally Posted by sderosa518 View Post
    Any hint on how to solve it?

    Should I factor a 3 out or factoriztion (x-1)(x+1)
    or just simply solve for zero
    do not ask me
    this is a quadratic equation
    you should know how to solve it
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    finale answer is 2, -14/3

    Correct???
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  10. #10
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    wrong
    you should get -3 and 1/3
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  11. #11
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    Curious how did you get?

    I use the quadratic formula!!!
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  12. #12
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    Quote Originally Posted by sderosa518 View Post
    Curious how did you get?

    I use the quadratic formula!!!
    I will be happy if i see your complete work
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  13. #13
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    F(x)= 3x^2+8x-3

    -8 -+Sqrt(8^2-4(3)(-3))
    ------------------------
    2(3)

    -8 +-sqrt(100)
    --------------
    6

    -8+-10
    ------- = 2, -14/3
    6

    Do you see where I got my answer. When you or if you show mean, I am going to feel stupid!??!
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  14. #14
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    Quote Originally Posted by sderosa518 View Post
    F(x)= 3x^2+8x-3

    -8 -+Sqrt(8^2-4(3)(-3))
    ------------------------
    2(3)

    -8 +-sqrt(100)
    --------------
    6

    -8+-10
    ------- = 2, -14/3
    6

    Do you see where I got my answer. When you or if you show mean, I am going to feel stupid!??!
    your work is good
    but your mistake is in the final answer
    you did not calculate it correctly
    there is two values
    \frac{-8-10}{6} and \frac{-8+10}{6}
    calculate them
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  15. #15
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    Silly mistake. I appreciate your help and your motivation towards me and my work.

    Regards
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