Given the function f(x)=x^4+8x^3+16x^2, determine all intervals on which f is decreasing.

Mathematics

1 answer:

ValentinkaMS [17]3 years ago

4 0

Answer:

see attachment

Step-by-step explanation:

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one number is equal to two times a second number. two times the first number plus two times the second number is 24. if you let

ziro4ka [17]

X = 2y
2x + 2y = 24
So if x = 2y that means 2x = 4y. Which means that 2x + 2y = 24 can be written as 4y + 2y = 24. Simplified to 6y = 24. Now we need to get 1y so we divide both sides by 6, 6y/6 = y and 24/6 = 4. so y = 4. so x= 2y can be written as x = 8.

5 0

3 years ago

Write the cubic polynomial function f(x)in expanded form with zeros −6,−5,and −1, given that f(0)=60

RSB [31]

Answer:

$f(x)=2x^{3}+24x^{2}+82x+60$

Step-by-step explanation:

we know that

The roots of the polynomial are the values of x when the value of the polynomial f(x) is equal to zero

The roots of the polynomial function are

x=-6 -----> (x+6)=0

x=-5 -----> (x+5)=0

x=-1 -----> (x+1)=0

The equation of the cubic polynomial is

$f(x)=a(x+6)(x+5)(x+1)$

where

a is the leading coefficient

Remember that

f(0)=60

That means ------> For x=0 the value of f(x) is equal to 60

substitute the value of x and the value of y in the function and solve for a

$60=a(0+6)(0+5)(0+1)$

$60=a(6)(5)(1)$

$60=30a$

$a=2$

$f(x)=2(x+6)(x+5)(x+1)$

Applying the distributive property

Convert to expanded form

$f(x)=2(x+6)(x+5)(x+1)\\\\f(x)=2(x+6)(x^{2}+x+5x+5)\\\\f(x)=2(x+6)(x^{2}+6x+5)\\\\f(x)=2(x^{3}+6x^{2}+5x+6x^{2}+36x+30)\\\\f(x)=2x^{3}+24x^{2}+82x+60$