Question 197410: Estimate the instantaneous rate of change:
a.for the function y = x^2 at the following x values:
i.x = 1
ii.x = 2
iii.x = 3
b.for the function y = x^3 at the following x values:
iv.x = 1
v.x = 2
vi.x = 3
c.Create two functions that can be developed from a) and b) that will give you the instantaneous rate of change without reducing the interval.
d.Use the reasoning from c) to find the instantaneous rate of change for:
iv.y = x^4 at x = 3
v.y = 3x^3 at x = 2
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Estimate the instantaneous rate of change:
a.for the function y = x^2 at the following x values:
The rate of change is 2x.
i.x = 1
m = 2
ii.x = 2
m = 4
iii.x = 3
m = 6
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b.for the function y = x^3 at the following x values:
The rate of change, m, is 3x^2
iv.x = 1
m = 3
v.x = 2
m = 12
vi.x = 3
m = 27
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c.Create two functions that can be developed from a) and b) that will give you the instantaneous rate of change without reducing the interval.
I did that, it's the 1st derivative.
For y = x^2, y' = 2x
For y = x^3, y' = 3x^2
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d.Use the reasoning from c) to find the instantaneous rate of change for:
iv.y = x^4 at x = 3
y' = 4x^3
m at 3 = 108
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v.y = 3x^3 at x = 2
y' = 9x^2
m at 2 = 36
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