A few questions

Question

g(x) x y 0 0 2 π 0 −2 2π 0

h(x) = 2 sin x + 3

Which function has the greatest rate of change on the interval from x = 0 to x = ?

 f(x)

 g(x)

 h(x)

 All three functions have the same rate of change.

Answer 1

Function f(x) = (0, 0), (pi/2, 4), (pi,0) , (3pi/2, -4) (2pi, 0)

g(x) = (0,0), (pi/2,4), (pi,0) (3pi/2,-4) , (2pi,0)

h(x) = 2 sin(x) + 3

find the average rate for each function on the interval x = 0 to x = pi/2.

Average rate for Function f(x):

Average rate = dy/dx =( y₂ - y₁)/(x₂ - x₁) = (4 - 0) / (pi/2 - 0) = 8pi

Average rate for Function g(x):

Average rate = dy/dx =( y₂ - y₁)/(x₂ - x₁) = (2 - 0) / (pi/2 - 0) = 4pi

Average rate for Function h(x):

h(x) = 2 sinx + 3

h(0) = 2 sin(0) + 3 = 3

h(pi/2) = 2 sin(pi/2) + 3 = 2 + 3 = 5

Average rate = dy/dx =( y₂ - y₁)/(x₂ - x₁) = (5 - 3) / (pi/2 - 0) = 2 /pi/2 = 4pi

Therfore , f(x) has the greatest rate of change on the interval form x = 0 to x = pi/2.

Option 1 is correct choice.