Need help with this question, I'm not sure what to do, so the steps to solve the question would be appreciated.

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anonymous · Answer

attachment

anonymous · Answer

@amistre64, @satellite73 or @freckles  can one of you guys help?

anonymous · Answer

i closed the question :( ill open another one

amistre64 · Answer

is f(x) got a hole at x=3?  or a asymptote?

amistre64 · Answer

by definition of a derivative,  it is the left and right limits as x goes to 3

anonymous · Answer

It does not tell me if its a whole or asymptote

amistre64 · Answer

oh it does ... you actually have to see it

anonymous · Answer

Is it a hole?

anonymous · Answer

since f(x) =6 when x=3?

amistre64 · Answer

f(x) = (x^2-9)/(x-3)

if the bottom is a factor of the top, then its removable

when x=3 we get 0/0   thereofre x-3 is a factor of the top and the bottom

f(x) can be considered equivalent to x+3

amistre64 · Answer

the piecewise simply fills in the hole to make a complete line and the whole of it makes it equal to x+3

anonymous · Answer

ok, so what does F′(3) equal? do i plug 3 into x=3?

amistre64 · Answer

no, lets say f(x) is your piecewise defined function,  and say g(x) = x+3

f(x) = g(x)  for all xs

therefore the derivative of g(x) is the same as f(x)

amistre64 · Answer

what is the derivative of x+3?

anonymous · Answer

that would be 1

amistre64 · Answer

then at x=3, the derivative is 1

anonymous · Answer

oh ok, so 1 is my answer?

amistre64 · Answer

id say so yes.

even if we didnt have the equality ... the slope from the left and right as x approaches 3 is 1

anonymous · Answer

ok, thank you soo much! i now understand the question. thank you again!!

amistre64 · Answer

youre welcome