1. A spherical balloon is being inflated so that itsvolume increases at a rate of 1200cm^3 per minute. How fast is itsradius increasing at the moment when the radius is 20cm? Recallthat the volume of a sphere is given by V = 4/3Ï€r^3
2. Which of the following is the linear approximation ofthe function f ( x ) = 2e^sin (7x) at x = 0?
Group of answer choices
y=cosâ¡(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 ) iscontinuous 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 functionh ( 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 productxy?
Group of answer choices
12
−72
0
−24
−144
