Question 10(Multiple Choice Worth 1 points) (04.02 LC) What is the x-coordinate of the solution to the following system of equat
1 answer:
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Answer:
The fifth degree Taylor polynomial of g(x) is increasing around x=-1
Step-by-step explanation:
Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:
and when you do its derivative:
1) the constant term renders zero,
2) the following term (term of order 1, the linear term) renders: since the derivative of (x+1) is one,
3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero
Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is: as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1
I hope this helps you
Write the polynomial as an equation.
y
=
x
3
−
2
x
2
−
3
x
+
6
y
=
x
3
-
2
x
2
-
3
x
+
6
To find the roots of the equation, replace
y
y
with
0
0
and solve.
0
=
x
3
−
2
x
2
−
3
x
+
6
0
=
x
3
-
2
x
2
-
3
x
+
6
Replace
y
y
with
0
0
and solve for
x
x
.
Tap for more steps...
x
=
2
,
√
3
,
−
√
3
x
=
2
,
3
,
-
3
The result can be shown in multiple forms.
Exact Form:
x
=
2
,
√
3
,
−
√
3
x
=
2
,
3
,
-
3
Decimal Form:
x
=
2
,
1.73205080
…
,
−
1.73205080
…
y
=
x
3
−
2
x
2
−
3
x
+
6
y
=
x
3
-
2
x
2
-
3
x
+
6
To find the roots of the equation, replace
y
y
with
0
0
and solve.
0
=
x
3
−
2
x
2
−
3
x
+
6
0
=
x
3
-
2
x
2
-
3
x
+
6
Replace
y
y
with
0
0
and solve for
x
x
.
Tap for more steps...
x
=
2
,
√
3
,
−
√
3
x
=
2
,
3
,
-
3
The result can be shown in multiple forms.
Exact Form:
x
=
2
,
√
3
,
−
√
3
x
=
2
,
3
,
-
3
Decimal Form:
x
=
2
,
1.73205080
…
,
−
1.73205080
…