Use f(x) = (x³ + 1) at x = 3. We want to find a value of del x small enough that graph of the function looks like a straight line on the region from 5* del x before the x-value to 5* del x after the x-value. Graph the function in this region and find the slope of the corresponding secant line. a. As our default we will look at del x = 0.001. Build a table and fill in the missing data from the table. f(x) X 2.998 2.999 3₂ b. Estimate the derivative by finding the slope of the secant when del a takes the values 0.1, 0.01, 0.001, 0.0001, -0.1, -0.01, -0.001, and -0.0001. Give a value of the limit of the slope. limit= c. Use the calculator approximation to estimate the slope of the tangent. f'(3) = d. Find the corresponding value of the marginal function marginal f(x + 1). Marginal f(3+1) =
Use f(x) = (x³ + 1) at x = 3. We want to find a value of del x small enough that graph of the function looks like a straight line on the region from 5* del x before the x-value to 5* del x after the x-value. Graph the function in this region and find the slope of the corresponding secant line. a. As our default we will look at del x = 0.001. Build a table and fill in the missing data from the table. f(x) X 2.998 2.999 3₂ b. Estimate the derivative by finding the slope of the secant when del a takes the values 0.1, 0.01, 0.001, 0.0001, -0.1, -0.01, -0.001, and -0.0001. Give a value of the limit of the slope. limit= c. Use the calculator approximation to estimate the slope of the tangent. f'(3) = d. Find the corresponding value of the marginal function marginal f(x + 1). Marginal f(3+1) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Use f(x) = (x³ + 1) at x = 3.
We want to find a value of del x small enough that graph of the function looks like a straight line on the region from 5* del x before the x-value
to 5 * del x after the x-value. Graph the function in this region and find the slope of the corresponding secant line.
a. As our default we will look at del x = 0.001. Build a table and fill in the missing data from the table.
X
2.998
2.999
3
f(x)
b. Estimate the derivative by finding the slope of the secant when del x takes the values 0.1, 0.01, 0.001, 0.0001, -0.1, -0.01, -0.001, and
-0.0001. Give a value of the limit of the slope.
limit=
c. Use the calculator approximation to estimate the slope of the tangent.
f' (3) =
d. Find the corresponding value of the marginal function marginal f(x + 1).
Marginal f(3+1) =
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