The following table gives values of the differentiable function y=f(x).

x 0 1 2 3 4 5 6 7 8 9 10
y -5 -7 -6 -4 2 -1 -3 -4 -5 -6 -8
estimate the x-values of critical points of f(x) on the interval 0 < x < 10. classify each critical point as a local maximum, local minimum, or neither.
(enter your critical points as comma-separated xvalue, classification pairs. for example, if you found the critical pointsx = -2and x = 3, and that the first was a local minimum and the second neither a minimum nor a maximum, you should enter (-2,min), (3,neither). enter none if there are no critical points.)

critical points and classifications:

now assume that the table gives values of the continuous function y=f'(x) (instead of f( estimate and classify critical points of the function f(x).

critical points and classifications:

answer:

step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.