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

a.)The only extrema point is (0, 25).
b.)No local extrema exist.
c.)The local and global extrema are: (1, 0), (3, 16) and (5, 0)
d.)No global extrema exist.

Question

antlayug antlayug

13-06-2017
Mathematics

contestada

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

a.)The only extrema point is (0, 25).
b.)No local extrema exist.
c.)The local and global extrema are: (1, 0), (3, 16) and (5, 0)
d.)No global extrema exist.

Respuesta :

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jdoe0001 jdoe0001 · Answer 1 · 2017-06-13T02:47:00+02:00

[tex]\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}[/tex]

For the polynomial function ƒ(x) = x4 − 12x3 + 46x2 − 60x + 25, find all local and global extrema. a.)The only extrema point is (0, 25). b.)No local extrema exist. c.)The local and global extrema are: (1, 0), (3, 16) and (5, 0) d.)No global extrema exist.

Respuesta :

Otras preguntas

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

a.)The only extrema point is (0, 25).
b.)No local extrema exist.
c.)The local and global extrema are: (1, 0), (3, 16) and (5, 0)
d.)No global extrema exist.