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Tpy6a [65]
4 years ago
6

Functions f(x) and g(x) are shown below:.

Mathematics
1 answer:
kobusy [5.1K]4 years ago
3 0
       First we will find the derivative of each function and equate it to zero.
       f` ( x ) = 6 x + 12
       6 x + 12 = 0
       6 x = - 12
       x = - 2
       f ( - 2 ) 0 12 - 24 + 16 = 4
       f ( x ) min = 4
       g` ( x ) = 4 cos (  2 x - π )
       4 cos ( 2 x - π ) = 0
       cos ( 2 x - π ) = 0
       2 x - π = 3π / 2
       2 x = 5π /2
       x = 5π/4
       g ( 5π/4 ) = 2 sin ( 5π/2 - π ) + 4 = 2 ( sin 3π/2 ) + 4 = -2 + 4 = 2
       g ( x ) min = 2 ( this is the smallest minimum value )
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In Problems 23–30, use the given zero to find the remaining zeros of each function
Talja [164]

Answer:

x =  2i, x = -2i and x = 4 are the roots of given polynomial.

Step-by-step explanation:

We are given the following expression in the question:

f(x) = x^3 - 4x^2+ 4x - 16

One of the zeroes of the above polynomial is 2i, that is :

f(x) = x^3 - 4x^2+ 4x - 16\\f(2i) = (2i)^3 - 4(2i)^2+ 4(2i) - 16\\= -8i+ 16+8i-16 = 0

Thus, we can write

(x-2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Now, we check if -2i is a root of the given polynomial:

f(x) = x^3 - 4x^2+ 4x - 16\\f(-2i) = (-2i)^3 - 4(-2i)^2+ 4(-2i) - 16\\= 8i+ 16-8i-16 = 0

Thus, we can write

(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Therefore,

(x-2i)(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16\\(x^2 + 4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Dividing the given polynomial:

\displaystyle\frac{x^3 - 4x^2 + 4x - 16}{x^2+4} = x -4

Thus,

(x-4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

X = 4 is a root of the given polynomial.

f(x) = x^3 - 4x^2+ 4x - 16\\f(4) = (4)^3 - 4(4)^2+ 4(4) - 16\\= 64-64+16-16 = 0

Thus, 2i, -2i and 4 are the roots of given polynomial.

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Answer:

Exterior Angle = 36 degrees

Step-by-step explanation:

<u><em>Each interior angle of a regular decagon measures 144 degrees.</em></u>

=> <u><em>We'll subtract 144 from 180 to get the measure of the exterior angle.</em></u>

=> Exterior Angle = 180-144

=> Exterior Angle = 36 degrees

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