As you did in exponential derivatives, your task is to find a formula for finding the slope at any point of y = 2². Start by creating a table like the one shown here. II 1 2 3 4 9/1 12 9/2 Derivative (291 22 21 Use the secant method that we used in Exponential slopes: • For each z in the 2₁ column, find the y value that goes with it; • Pick another z value very, very, very close by and finds its y value; Get a good approximation for the derivative of the function at the point on the graph y = z² by finding the slope of the secant between these two points. Do this for at least three more x values. See if you can find a formula for finding the derivative at any point in terms of either the r or y value.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
As you did in exponential derivatives, your task is to find a formula for finding the slope at
any point of y = 2².
Start by creating a table like the one shown here.
IL
1
2
3
4
3/1
12
Y2
Derivative (2)
Use the secant method that we used in Exponential slopes:
• For each z in the ₁ column, find the y value that goes with it;
• Pick another z value very, very, very close by and finds its y value;
• Get a good approximation for the derivative of the function at the point on the graph
y = z² by finding the slope of the secant between these two points.
Do this for at least three more x values.
See if you can find a formula for finding the derivative at any point in terms of either the
or y value.
Transcribed Image Text:As you did in exponential derivatives, your task is to find a formula for finding the slope at any point of y = 2². Start by creating a table like the one shown here. IL 1 2 3 4 3/1 12 Y2 Derivative (2) Use the secant method that we used in Exponential slopes: • For each z in the ₁ column, find the y value that goes with it; • Pick another z value very, very, very close by and finds its y value; • Get a good approximation for the derivative of the function at the point on the graph y = z² by finding the slope of the secant between these two points. Do this for at least three more x values. See if you can find a formula for finding the derivative at any point in terms of either the or y value.
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