Question

Hi can u you help me with this Curve sketching question. I just need to know what are the list of things i have to find to be able to show full working and sketch the graph afterwards. Thanks

Answer 1

like ok i know i have to find the x and y intercepts, vertical and horizontal intercepts but then what? thanks

Answer 2

well the curve has verrtical and horizontal asymptotes... and there are 2 sections to the curve...

you need to find the 1st detivative

then 2nd derivative

find the stationary points in the 1st derivative and test them in the 2nd derivative to determine there nature.

solve the 2nd derivative to see if there are any points of inflection.

if there are, check either side so see if there is a change in concavity

I think hat covers it.

Answer 3

can you help me with the derivatives part ?

Answer 4

so f(x)"=-10x+3 and g(x)"=4x ... now that is the first derivatives

Answer 5

the second i believe is ((-10x+3)(2x^2-5))-((4x)(-5x^2+3x))/(2x^2-5)^2

Answer 6

im i on the right track? @campbell_st

Answer 7

well the function needs the quotient rule to get the derivatives....

Answer 8

after solving the derivative i got (-6x^2+50x-15)/(2x^2-5)^2

Answer 9

the curve has 3 parts will a horizontal asymptote at y = -5/2 and verticals at

\[x = \pm \sqrt{\frac{5}{2}}\]

so it looks a bit like