Question

help even just one of the three questions - it says
"do a calculus based analysis for the properties of the function, then use the results to sketch the graph
1.)y=x^4-2x^2
2.)y=(x+1)^2/x
3.)f(x)=x^3-6x^2+12x"

Answer 1

take the derivative and use it to find intervals where the function is increasing/decreasing, max and min and concave up/concave down (2nd derivative)...

Answer 2

:)

Answer 3

lol, I know what you meant...

Answer 4

\[y'=4x ^{3}-4x\]

Answer 5

yes

Answer 6

then?

Answer 7

roots of y' at 0 1 and -1
so there are your max.s and min.s
check the intervals between for the value of y' ...

Answer 8

if positive then y is increasing, if negative decreasing...

Answer 9

what are the root for?

Answer 10

roots of y' are the extrema of y

Answer 11

am i gonna subs it to x?

Answer 12

no...look:

Answer 13

if, for example, you find that y' is positive to the left of -1 and negative to the right of -1 (between -1 and 0), then you know that y must have a max at x=-1