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BartSMP [9]
3 years ago
9

For the polynomial function ƒ(x) = x4 − 12x3 + 46x2 − 60x + 25, find all local and global extrema.

Mathematics
1 answer:
rodikova [14]3 years ago
4 0
\bf f(x)=x^4-12x^3+46x^2-60x+25\\\\
-------------------------------\\\\
\cfrac{df}{dx}=4x^3-36x^2+92x-60\implies 0=4x^3-36x^2+92x-60
\\\\\\
0=x^3-9x^2+23x-15\impliedby \textit{doing some synthetic division with 5}
\\\\\\
0=(x^2-4x+3)(x-5)\implies 0=(x-3)(x-1)(x-5)\\\\
-------------------------------\\\\
\begin{cases}
f(1)=0\leftarrow minimum&1,0\\
f(3)=16\leftarrow maximum&3,16\\
f(5)=0\leftarrow minimum&5,0
\end{cases}\impliedby \textit{3 extrema, locals and globals}
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Answer:

4/5

Step-by-step explanation:

8/15 = 8/15

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11/15 = 11/15

We see that the pattern is that the terms increase by 1/15 as they move up.

Thus, the next term in the sequence is 12/15, which can be simplified to 4/5.

Let me know if this helps!

3 0
2 years ago
1.94x - 10/8x + 4.32 = [2(1.15x+8.5)]
kipiarov [429]
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3 years ago
Y=x+2<br> 3x+3y=6<br> solving systems by substitution
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2

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.

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−

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+

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3

x

+

3

y

=

6

3

x

+

3

y

=

6

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y

y

in

3

x

+

3

y

=

6

3

x

+

3

y

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with

−

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2

-

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2

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y

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−

x

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2

y

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(

−

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2

)

=

6

3

x

+

3

(

-

x

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2

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6

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3

x

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3

(

−

x

+

2

)

3

x

+

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(

-

x

+

2

)

.

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−

x

+

2

y

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-

x

+

2

6

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6

6

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6

Since

6

=

6

6

=

6

, the equation will always be true.

y

=

−

x

+

2

y

=

-

x

+

2

Always true

Remove any equations from the system that are always true.

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=

−

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2

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Step-by-step explanation:

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