Question

1. 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

2. 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 ].

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 product xy?

Group of answer choices

12

−72

0

−24

−144

Answer 1