Question

Compare the functions below f(x)=3^x+2 g(x)=20x+4 h(x)=2x^2+5x+2 select the true statements 1. Over the interval [2,3], the average rate of change of g is lower than that of both f and h 2. As x increases on the interval [0,infinity), the rate of change of g eventually exceeds the rate of change of both f and h 3. When x = 4, the value of f(x) exceeds the values of both g(x) and h(x) 4. When x=8, the value of h(x) exceeds the values of both f(x) and g(x) 5 as x increases on the interval [0,infinity), the rate of change of f eventually exceeds the rate of change of both g and h 5 a quantity increasing exponentially eventually exceeds a quantity growing quadratically or linearly

Answer 1

Answer:

Step-by-step explanation:

Given are three functions, f, g and h.  We are to check the validity of the statements from 1 to 5

1) Avg rate of change of functions in the interval [2,3]

$f(x) = f(3)-f(2) =29-11=18$

$g(x) = g(3)-g(2) =64-44=20$

$h(x) = h(3)-h(2) = 15$

False

2) False, From the graph given we find that it is false

3) True since f(4) is higher than other function value at 4.

4) h(8) = 128+40+2 =170.   f(8) = 6563

Hence false.

5) f'(x) =3^x lnx:  g'(x) = 20:  h'(x) = 4x+5

False because when x=1, rate of change of f = 0<g'(x)

Last statement  a quantity increasing exponentially eventually exceeds a quantity growing quadratically or linearly

is true

Answer 2

This exercise is designed to ascertain which statements are TRUE according to the following functions:

• f(x)=$3^{x+2}$
• g(x)=20x+4
• h(x)=2x²+5x+2

What is a Mathematical Function?

A mathematical function refers to the expression of a law involving dependent and independent variables in a mathematical way. Three functions, f, g, and h, are given. From 1 to 5, we must check the reliability of the statements.

A) It is to be noted that the average rate of change of functions in the interval [2,3] is False;

f(x) = f(3) - f(2)

= 29-11

= 18;

g(x) = g(3) -g(2)

= 64-44

= 20

h(x) = h(3) - h(2)

= 15

Hence this assertion is False.

B)  From the graph given, it is right to state that this the statement is false

C) It is right to state that this is TRUE. This is because:

f(4) is higher than other function values at 4.

D) h(8) = 128+40+2 =170.   f(8) = 6563

Therefore, the statement is false.

E) f'(x) =3ˣ lnx:  g'(x) = 20:  h'(x) = 4x+5

We must regard this as False because when x=1, the rate of change of f = 0<g'(x)

Given the components mentioned, it is TRUE that a quantity expanding exponentially eventually surpasses a quantity developing quadratically or linearly in the last statement.

Learn more about functions at:

brainly.com/question/12739882

#SPJ5