Question

1. A spherical balloon is being inflated so that its volume increases at a rate of 1200cm^3 per minute. How fast is its radius increasing at the moment when the radius is 20cm? Recall that the volume of a sphere is given by V = 4/3πr^3

2. Which of the following is the linear approximation of the function f ( x ) = 2e^sin (7x) at x = 0?

Group of answer choices

y=cos⁡(7)x+2

y=7x+2

y=14x+2

y=2x+7

y=e^7x+14

3. Recall that Rolle's Theorem begins, ``If f ( x ) is continuous on an interval [ a , b ] and differentiable on ( a , b ) and ___________, then there exists a number c …'' Find all values x = c that satisfy the conclusion of Rolle's Theorem for the function h ( x ) = x^3 − 7x − 9 on the interval [ − 2 , − 1 ].

4.If x and y are two real numbers such that 8x − y = 48, what is the smallest possible value of their product xy?

Group of answer choices

12

−72

0

−24

−144

Answer 1