Question

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

The relative maximum is at (–6, 216) and the relative minimum is at (2, –40).

The relative maximum is at (–6, 40) and the relative minimum is at (2, –216).

The relative maximum is at (6, 216) and the relative minimum is at (–2, –40).

The relative maximum is at (6, 40) and the relative minimum is at (–2, –216).

Answer 1

relative max and mins are usually where the slope of the function is zero.
1) take the derivative of x^3+6x^2 and set to zero and solve for the zeros.
2) the relative max should have an x value smaller than the relative min. because the cubic goes to +infinity at x=+infinity and -infinity at x = -infinity

Answer 2

so , im confused . .. would it be the 2nd one ?

Answer 3

are you sure you wrote the question down right?

Answer 4

yes, lol. i just copied and pasted the question .

Answer 5

i think that there should be an x after -36
i.e.
\[x^3+6x^2-36x\]

because this derivative is
\[3x^2+12x-36\]
\[3(x^2+4x-12)\]
which factors to
\[3(x+6)(x−2)\]

which gives zeros at x=-6 and 2 which fit your answers much better.
In this case the max is at -6 and the min at 2

but the y values are wrong and I usually am wrong when I accuse the book so...

Answer 6

also the points given in the answer don't lie on the function they give.
when x=6 y =396
when x = -6 y = -36