Question

Please help! Will FAN AND MEDAL!

Which of the following functions grows the fastest as x grows without bound?

a. f(x) = x2
b. g(x) = x2 + 5x
c. h(x) = the square root of the quantity x raised to the 4th power plus 2 times x
d. They all grow at the same rate.

Answer 1

Can you please help? @Directrix @mathmale

Answer 2

@Agl202

Answer 3

Any clue? @Agl202

Answer 4

@Directrix @dmezzullo Perhaps we could use some help here :)

Answer 5

Can you please help? @mathmale

Answer 6

First, Aryana, a bit of housekeeping:

a. f(x) = x2
b. g(x) = x2 + 5x
c. h(x) = the square root of the quantity x raised to the 4th power plus 2 times x

It's important to express exponentiation with the ^ symbol: f(x)=x^2; g(x)=x^2+5x, \[h(x)=\sqrt{x^4+2x}\]

Answer 7

a. x^2
b. x^2+5x
c. yes your equation is correct

Answer 8

One way of doing this would be to find the derivative of each function, as the derivative represents the instantaneous rate of change. Then you could rank order the derivatives from smallest to largest and thus answer the question at hand.

a) the derivative with respect to x of x^2 is 2x; Find
b) the deriv of x^2+5x and
c) the deriv. of sqrt(x^4+2x).

Compare them, assuming that x increases at the same rate for all of them.

Answer 9

?? I am sorry but I do not understand?

Answer 10

@mathmale

Answer 11

@mathmale

Answer 12

"Which of the following functions grows the fastest as x grows without bound?" All of the functions are increasing on their domains. The question here is: WHICH function increases fastest with x? The measure of rate of change is the DERIVATIVE. That's why I'm asking you to differentiate each of the 3 given functions.

Answer 13

Derivative = instantaneous rate of change. Extremely important concept!

Answer 14

rate of change = how fast something is increasing or decreasing as the independent variable increases.

e. g., 50 mph: the distance traveled increases by 50 miles for each hour on the road.

Answer 15

Okay so how do I find that out? Do I have to plug something into x?

Answer 16

@mathmale

Answer 17

Can you please help? @agent0smith

Answer 18

Do you know how to find derivatives...?

Answer 19

I believe the answer is a?

Answer 20

Otherwise you can kinda compare them by looking at the highest power of x in each option, since the highest powers will dominate as x grows.

Highest power of x in a is x^2,

in b it's also x^2,

and in c, it's effectively \[\large \sqrt {x^4}\]which can be simplified...

Answer 21

to x^2 so the answer is actually D. Since they all have the same power right?

Answer 22

Yes

Answer 23

Thank you. Can you help me with two more?

Answer 24

?? @agent0smith

Answer 25

No, I still have to leave, I only came back for a while

Answer 26

Please post each new problem separately.

I'm curious: Why did you not answer agent0smith's question, "Do you know how to find derivatives...?" He was trying to determine the level of explanation that would be appropriate here.