Question

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

Answer 1

in #2 the equation is xe^x not xex sorry

Answer 2

@welshfella

Answer 3

hmm - i'd need to refresh my knowledge of the Mean Value Theorem..

Answer 4

Anyone understand lol ?

Answer 5

Do you understand the bottom question then?

Answer 6

for the bottom question you need to find an expression for the velocity
its ds/dt

Answer 7

so finf the derivative of x e^x

Answer 8

use the product rule

Answer 9

the derivative of the equation is e^x(x+1)

Answer 10

right

so equate that to zero

Answer 11

x=-1

Answer 12

correct

Answer 13

So it would only be 1 time?

Answer 14

yep

Answer 15

Thank you!!!

Answer 16

as you no e^x cannot be zero

Answer 17

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