1. 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
2. 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 ].
3. At x = 1, the function g( x ) = 5x ln(x) −3/x
is . . .
Group of answer choices
has a critical point and is concave up
decreasing and concave up
decreasing and concave down
increasing and concave up
increasing and concave down
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
