tmagloire1
  • tmagloire1
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
Mathematics
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
tmagloire1
  • tmagloire1
in #2 the equation is xe^x not xex sorry
tmagloire1
  • tmagloire1
@welshfella
welshfella
  • welshfella
hmm - i'd need to refresh my knowledge of the Mean Value Theorem..

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tmagloire1
  • tmagloire1
Anyone understand lol ?
tmagloire1
  • tmagloire1
Do you understand the bottom question then?
welshfella
  • welshfella
for the bottom question you need to find an expression for the velocity its ds/dt
welshfella
  • welshfella
so finf the derivative of x e^x
welshfella
  • welshfella
use the product rule
tmagloire1
  • tmagloire1
the derivative of the equation is e^x(x+1)
welshfella
  • welshfella
right so equate that to zero
tmagloire1
  • tmagloire1
x=-1
welshfella
  • welshfella
correct
tmagloire1
  • tmagloire1
So it would only be 1 time?
welshfella
  • welshfella
yep
tmagloire1
  • tmagloire1
Thank you!!!
welshfella
  • welshfella
as you no e^x cannot be zero
Loser66
  • Loser66
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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