Mathematics, 26.12.2019 18:31 jamiahharrell21

Consider the function f ( x ) = − 2 x 3 + 27 x 2 − 108 x + 9 . for this function there are three important open intervals: ( − [infinity] , a ) , ( a , b ) , and ( b , [infinity] ) where a and b are the critical numbers. find a and b

Answers: 1

Show answers

Answers

Answer from: hunter196

A=3 and B=6

Step-by-step explanation:

Increasing and Decreasing Intervals of Functions

Given f(x) as a real function and f'(x) its first derivative.

If f'(a)>0 the function is increasing in x=a

If f'(a)<0 the function is decreasing in x=a

If f'(a)=0 the function has a critical point in x=a

As we can see, the critical points may define open intervals where the function has different behaviors.

We have

f ( x ) = - 2 x^3 + 27 x^2 - 108 x + 9

Computing the first derivative:

f' ( x ) = - 6 x^3 + 54 x - 108

We find the critical points equating f'(x) to zero

- 6 x^3 + 54 x - 108=0

Simplifying by -6

x^2 -9 x +18=0

We get the critical points

$x=3,\ x=6$

They define the following intervals

$(-\infty,3),\ (3,6),\ (6,+\infty)$

Thus A=3 and B=6

Answer from: Quest

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

Answer from: Quest

5x + 5

step-by-step explanation:

you should always add the diagrams and graphs we cannot see. this particular question is kind of borderline because we can make a graph for you.

(f + g)x = -x^2 +3x + 5 + x^2 + 2x

(f + g)x = 5x + 5

the graph of z = 5x + 5 is shown below. always use desmos when in doubt.

Another question on Mathematics

Mathematics, 21.06.2019 15:30

Gretchen is setting up for a banquet. she has 300 chairs and needs to distribute them evenly among t tables. how many chairs should she put at each table? write your answer as an expression.

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

If the discriminant if a quadratic equation is 4 which statement describes the roots?

Answers: 3

Answer

Mathematics, 21.06.2019 21:30

Consider a bag that contains 220 coins of which 6 are rare indian pennies. for the given pair of events a and b, complete parts (a) and (b) below. a: when one of the 220 coins is randomly selected, it is one of the 6 indian pennies. b: when another one of the 220 coins is randomly selected (with replacement), it is also one of the 6 indian pennies. a. determine whether events a and b are independent or dependent. b. find p(a and b), the probability that events a and b both occur.

Answers: 2

Answer

Mathematics, 21.06.2019 23:40

Binh says the point of intersections is (0,-3) which statements identify the errors binh made , check all that apply

Answers: 2

Answer

You know the right answer?

Consider the function f ( x ) = − 2 x 3 + 27 x 2 − 108 x + 9 . for this function there are three imp...

Questions