Question

what is the relative maximum and minimum of the function.
f(x)=x^3+6x^2-36

Answer 1

I'll do this one, and maybe you can show where you get stuck on the others, if you do. If you just want confirmation of your answers, just show what you get.

max and min occur where f'(x) = 0

f'(x) = 3x^2 + 12x
= 3x(x+4)

f'=0 when x=0 or x = -4.

f(-4) = -4
f(0) = -36

Now, the question is, which is max, which is min?

Knowing what you do about the shape of cubics, it should be clear which is which.

The definitive way is to check the second derivative.

f''(x) = 6x+12
If f'' < 0, it's a max
If f'' > 0, it's a min.

Check it out, and you're done.

Answer 2

I don't understand

Answer 3

ok. I see this is for an algebra class, not calculus. In that case, things are a bit less straightforward. What is the subject of your current chapter? Unless you have some numerical tools at your command, I don't know of a general way to find maxima and minima for cubics and higher-order.

Answer 4

dividing polynomials possible answers are
max(-6,216)minimum(2,-40)
(-6,40) (2,-216)
(6,216) (-2,-40)
(6,40) (-2,-216)

Answer 5

oh, well. If they give you choices, just plug in the x values and see what pops out. However, the choices given do not appear to me to be correct for that polynomial.

visit wolframalpha.com and type in your function. It will show a graph, and you can see that the relative max and min are as I calculated above.