(5 points) Mark each statement below as true or false by circling

T

or

F

. No justification is necessary.\ T F If

c

is critical number of a function

f

and also

f^('')(c)=0

, then by the Second Derivative Test, it follows that

f

achieves neither a local maximum nor a local minimum at

x=c

.\ T F The absolute maximum value of a continuous function

f(x)

defined on a closed interval

a,b

can only be realized at an endpoint or

x=b

or at a point where the graph of

f

has a horizontal tangent.\ T F If

h

is continuous, decreasing, and concave down for all

x

, then

h(x)

must be negative for some sufficiently large value of

x

.\ T F A recommended initial "guess" when using Newton's method to solve the equation

f(x)=0

is an

x_(1)

such that

f^(')(x_(1))

is very close to zero.

13. (5 points) Mark each statement below as true or false by circling T or F. No justification is necessary. T I c is critical number of a function f and also f(c)=0, then by the Second Derivative Test, it follows that f achieves neither a local maximum nor a local minimum at x=c. T F The absolute maximum value of a continuous function f(x) defined on a closed interval [a,b] can only be realized at an endpoint (x=a or x=b) or at a point where the graph of f has a horizontal tangent. T If h is continuous, decreasing, and concave down for all x, then h(x) must be negative for some sufficiently large value of x. T F A recommended initial "guess" when using Newton's method to solve the equation f(x)=0 is an x1 such that f(x1) is very close to zero