Math 144, Exam 4 tf exam complete with verified solutions

Math 144, Exam 4 t/f exam
complete with verified
solutions

Let f(x) be a continuous and differentiable
function. Then f(x) decreases at x=c if f'(c) > 0 -
answer false


Let c be a critical value of the continuous and
differentiable function f(x) . If f'(x)>0 to the left of
x=c and f'(x)<0 to the right of x=c , then f(c) is a
relative maximum - answer true


Let c be a critical value of the continuous and
differentiable function f(x) . If f'(x)<0 to the left of
x=c and f'(x)>0 to the right of x=c , then f(c) is
neither a relative maximum nor a relative minimum
- answer false


let f(x) be a continuous function such that f'(x)
increases when x=c. Then f(x) is concave up when
x=c - answer true


let f(x) be a continuous function such that f' > 0.
Then f(x) is concave up when x=c - answer false

, Let f(x) be a continuous and differentiable
function. If f(x) >0 for all x in the domain of f(x),
then f(x) increases for all x in its domain - answer
false


let c be in domain of f(x). If f(c) less than or equal
f(x) for all x sufficiently close to c, then f(c) is a
relative minimum - answer true


Let c be a critical value of the continuous and
differentiable function f(x) . If f'(x)>0 to the left of
x=c and f'(x)<0 to the right of x=c , then f(c) is a
relative minimum - answer false


let f(x) be a continuous function such that f''(7) =
0. then f(x) must have a point of inflection when
x=7 - answer false


let f(x) be a continuous function. According to the
second derivative test, if f''(c) <0 and f'(c) = 0,
then f(x) has a relative maximum when x=c -
answer true


let c be in domain of f(x). If f(c) greater than or
equal f(x) for all x sufficiently close to c, then f(c)
is a relative maximum - answer false