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A few questions

0 votes
sine curve with points at 0, 0 and pi over 2, 4 and pi, 0 and 3 pi over 2, negative 4 and 2 pi, 0

g(x)

x y
0 0
pi over 2 2
π 0
3 pi over 2 −2
0

h(x) = 2 sin x + 3



Which function has the greatest rate of change on the interval from x = 0 to x = pi over 2?

 f(x)

 g(x)

 h(x)

 All three functions have the same rate of change.

asked Aug 8, 2014 in ALGEBRA 2 by HelpPlease Rookie

1 Answer

0 votes

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.

answered Aug 8, 2014 by david Expert
edited Aug 8, 2014 by david

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