The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:
<span><span>x1 </span>= 0.42801</span>
<span><span>x2 </span>= −1.51414</span>
<span><span>x3 </span>= 3.08613</span>
x1 and x2 are in the desired interval [-2, 2]
f'(x) = 3x^2 - 4x - 4
so we have:
3x^2 - 4x - 4 = 0
<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6
x_1 = -4/6 = -0.66
x_ 2 = 2
According to Rolle's theorem, we have one point in between:
x1 = 0.42801 and x2 = −1.51414
where f'(x) = 0, and that is <span>x_1 = -0.66</span>
so we see that Rolle's theorem holds in our function.
Answer:
a=1 b=4 c=-5
Step-by-step explanation:
Perimeter is legnth +legnth + width + width or
P=2L+2W
L=2W
subsitute L=2W for L in P=2L+2W
P=2(2W)+2W
P=4W+2W
P=6W
we know that Perimiter=30 so
30=6W
divide both sides by 6
5=Width
subsitute W=5 for W in L=2W
L=2(5)
L=10
to check
10=2(10)+2(5)
30=20+10
30=30
checks
Legnght=10
Width=5
It is =8 00 8-0 I Ait gg ;8 00
O 0 0
V
0
