What is the average rate of change of the function f(x) = 2x2 + x + 5 over the interval −2 ≤ x ≤ 2?

16

Step-by-step explanation:

Given the function f(x) = 2x² + x + 5, the rate of change of the function is given as d{f(x)}/dx= 4x+1

Expressing the rate of change over an interval −2 ≤ x ≤ 2:

When x = -2

d{f(x)}/dx = 4(-2)+1

d{f(x)}/dx = -8+1

d{f(x)}/dx = -7

When x = 2

d{f(x)}/dx = 4(2)+1

d{f(x)}/dx = 8+1

d{f(x)}/dx = 9

Average rate of change = 9-(-7)

Average rate of change = 16

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

the answer

b. they are parallel and will never intersect.