We'll need to find the 1st and 2nd derivatives of F(x) to answer that question.
F '(x) = -4x^3 - 27x^2 - 48x - 16 You must set this = to 0 and solve for the
roots (which we call "critical values).
F "(x) = -12x^2 - 54x - 48
Now suppose you've found the 3 critical values. We use the 2nd derivative to determine which of these is associated with a max or min of the function F(x).
Just supposing that 4 were a critical value, we ask whether or not we have a max or min of F(x) there:
F "(x) = -12x^2 - 54x - 48 becomes F "(4) = -12(4)^2 - 54(4)
= -192 - 216
Because F "(4) is negative, the graph of the given
function opens down at x=4, and so we have a
relative max there. (Remember that "4" is only
an example, and that you must find all three
critical values and then test each one in F "(x).
<em>Answer:</em>
<em>2.133</em>
<em>Step-by-step explanation:</em>
<em>Hope this helps!</em>
Answer:
22.43
Step-by-step explanation:
three points ==> it's a triangle
so we will just have to calculate the length of each side
U & V has the same y-coordinate, which means UV is a horizontal line ==>
UV = 3 - (-2) = 5
V & W has the same x-coordinate, which means VW is a vertical line ==>
VW = 4 - (-4) = 8
UW is not a horizontal line nor a vertical line, so we will have to calculate it using distance formula
UW = sqrt { [3 - (-2)]^2 + [-4 - 4]^2 } = sqrt{25 + 64} = sqrt(89) ~~ 9.43
so the perimeter of the polygon is UV + VW + UW = 5 + 8 + 9.43 = 22.43
