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tmagloire1

  • one year ago

AP Calculus AB Help 1) If f(x) = |(x2 − 4)(x2 + 2)|, how many numbers in the interval [0, 1] satisfy the conclusion of the Mean Value Theorem? 2)A particle moves along the x-axis with position function s(t) = xex. How many times in the interval [−5, 5] is the velocity equal to 0? One Two Three More than three

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  1. tmagloire1
    • one year ago
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    in #2 the equation is xe^x not xex sorry

  2. tmagloire1
    • one year ago
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    @welshfella

  3. welshfella
    • one year ago
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    hmm - i'd need to refresh my knowledge of the Mean Value Theorem..

  4. tmagloire1
    • one year ago
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    Anyone understand lol ?

  5. tmagloire1
    • one year ago
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    Do you understand the bottom question then?

  6. welshfella
    • one year ago
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    for the bottom question you need to find an expression for the velocity its ds/dt

  7. welshfella
    • one year ago
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    so finf the derivative of x e^x

  8. welshfella
    • one year ago
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    use the product rule

  9. tmagloire1
    • one year ago
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    the derivative of the equation is e^x(x+1)

  10. welshfella
    • one year ago
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    right so equate that to zero

  11. tmagloire1
    • one year ago
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    x=-1

  12. welshfella
    • one year ago
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    correct

  13. tmagloire1
    • one year ago
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    So it would only be 1 time?

  14. welshfella
    • one year ago
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    yep

  15. tmagloire1
    • one year ago
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    Thank you!!!

  16. welshfella
    • one year ago
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    as you no e^x cannot be zero

  17. Loser66
    • one year ago
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    For the first one, the mean value theorem says \(f'(c) =\dfrac{f(b) -f(a) }{b-a}\) hence f'(c) =1 now, from the original one , since it is an absolute value function, we have f(0) =8, f(1) =9 and it is increasing on [0,1]. you can test it by take f'(c) and consider value of f'(0) and f'(1) to see it is increasing. So that only 1 value of c satisfy the mean value theorem

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