80 24c 80 C = 24 Write the 80 as the product of 5 and a power of 2. Write the 24 as a factorial. What pattern do you notice?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section: Chapter Questions
Problem 30P: In this problem you are asked to find a function that models in real life situation and then use the...
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8. In Problem 4, you should have found that for the fourth derivative P" (0) to equal
f (0), the value of c4 was given by
80
24c, = 80 > C4 =
24
Write the 80 as the product of 5 and a power of 2. Write the 24 as a factorial. What
pattern do you notice?
Additional info
4. Function f is also locally cubic and locally quartic at x = 0. Find equations for the
cubic and quartic functions,
P3(x) = Co + Cx + C2x² + C3x' and
P, (x) Co + Cx + Cx² + C3x' + Cx*,
that best fit f(x) at x = 0. For these equations, P3 (0) and P,(0) must equal f(0), and
the first three derivatives (for P3) or the first four derivatives (for P4) must equal the
corresponding derivatives of f at x = 0. How do the coefficients co, C, and c2 compare
with those for the quadratic and linear functions in Problems 2 and 3?
Transcribed Image Text:8. In Problem 4, you should have found that for the fourth derivative P" (0) to equal f (0), the value of c4 was given by 80 24c, = 80 > C4 = 24 Write the 80 as the product of 5 and a power of 2. Write the 24 as a factorial. What pattern do you notice? Additional info 4. Function f is also locally cubic and locally quartic at x = 0. Find equations for the cubic and quartic functions, P3(x) = Co + Cx + C2x² + C3x' and P, (x) Co + Cx + Cx² + C3x' + Cx*, that best fit f(x) at x = 0. For these equations, P3 (0) and P,(0) must equal f(0), and the first three derivatives (for P3) or the first four derivatives (for P4) must equal the corresponding derivatives of f at x = 0. How do the coefficients co, C, and c2 compare with those for the quadratic and linear functions in Problems 2 and 3?
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