1. Let g(z) = z² + z + 1. Show work to explain your reasoning for each of the following. (a) Find the average rate of change of g with respect to z for 2 < z < 7. (b) Draw a graph of the function g. In your graph, draw a line with slope the average rate of change of g with respect to z for 2 < z < 7. Write at least one sentence to explain why you know the line has the correct slope. (c) Find a formula for the average rate of change of g with respect to z for 2 < z < 2+h.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Let g(z) = z²+ z + 1. Show work to explain your reasoning for each of the following.
(a) Find the average rate of change of g with respect to z for 2 < z < 7.
(b) Draw a graph of the function g. In your graph, draw a line with slope the average
rate of change of g with respect to z for 2 < z < 7. Write at least one sentence
to explain why you know the line has the correct slope.
(c) Find a formula for the average rate of change of g with respect to z for 2 <z<
2+ h.
Transcribed Image Text:1. Let g(z) = z²+ z + 1. Show work to explain your reasoning for each of the following. (a) Find the average rate of change of g with respect to z for 2 < z < 7. (b) Draw a graph of the function g. In your graph, draw a line with slope the average rate of change of g with respect to z for 2 < z < 7. Write at least one sentence to explain why you know the line has the correct slope. (c) Find a formula for the average rate of change of g with respect to z for 2 <z< 2+ h.
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