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

2^2-4+6 is your answer

Answer 2

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