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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 xaxis 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
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 xaxis 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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tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0in #2 the equation is xe^x not xex sorry

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0hmm  i'd need to refresh my knowledge of the Mean Value Theorem..

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Anyone understand lol ?

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Do you understand the bottom question then?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0for the bottom question you need to find an expression for the velocity its ds/dt

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0so finf the derivative of x e^x

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0use the product rule

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0the derivative of the equation is e^x(x+1)

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0right so equate that to zero

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0So it would only be 1 time?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0as you no e^x cannot be zero

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0For the first one, the mean value theorem says \(f'(c) =\dfrac{f(b) f(a) }{ba}\) 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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