Question

Comparing functions?

Answer 1

Which function has the smallest rate of change from x = 0 to x = pi over 2?
f(x)

g(x)

h(x)

All three functions have the same rate of change over the given interval.

Answer 2

Find the average rate of change of each function in the interval [0, pi/2] and compare.

Answer 3

Okay, how can I do that?

Answer 4

Average rate of change of f(x) in [a,b] is: { f(b) - f(a) } / { b - a }

Answer 5

okayyyy

Answer 6

Could you help me with that though? like for the graph part

Answer 7

For the graph, you can read the y-values off of the graph.
g(pi/2) = 3; g(0) = 0.
Average rate of change of g(x) in [0, pi/2] is: { 3 - 0 } / { pi/2 - 0 } = 3 * 2 / pi = 6/pi

Answer 8

Okay thanks :)

Answer 9

You are welcome.

Answer 10

Would the answer be g(x) ?

Answer 11

What are the three rates of change you are getting?

Answer 12

Ugh I think i'm doing this all wrong because every time I always get different answers :(

Answer 13

f(x) = 3cos(2x - pi) - 1
f(pi/2) = 3cos(0) - 1 = 3 - 1 = 2
Average rate of change of f(x) in [0, pi/2] = 2 / (pi/2) = 4 / pi.

Average rate of change of g(x) in [0, pi/2] = 6/pi

h(x) = sin(x) - 4
h(pi/2) = sin(pi/2) - 4 = 1 - 4 = -3
Average rate of change of h(x) in [0, pi/2] = -3 / (pi/2) = -6 / pi.

We need to compare only their magnitudes (or absolute values):
4/pi or 6/pi or |-6/pi| = 6/pi ?

Answer 14

Ohhhh gotcha! That makes hella sense now :) Thanks mannn you're awesome!

Answer 15

So the lowest would be h(x) right?

Answer 16

You are welcome. Glad to be able to help.