Question

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Answer 1

(a) well start with the vertical asymptote

you need to solve for x

\[x -1 = 0\]

the horizontal asymptote is found by looking at the coefficients of the leading terms

numerator is -1 denominator is 1

both the numerator and denominator are the same degree so the horizontal asymptote is y = -1

(b) look at the 1st derivative, set it to zero and solve for x, this is a stationary point

to do this set the numerator to zero and solve

so you need to solve x - 5 = 0

test the solution in the 2nd derivative to determine the nature

(c) set the 2nd derivative to zero and solve for x.

so the numerator can be zero for the derivative to be zero

so solve

2x - 14 = 0

select values either side of the solution and check there is a change in concavity.

if so, you have a point of inflection.

hope it helps.

Answer 2

yes.. just pick values close and see what's happening... I think they go in the same direction on both sides... to plus infinity