Let f be a function whose Maclaurin series expansion. f(x)=3+12x+24x^2+32x^3+... Explain how you can determine f'(0), f''(0), and f'''(0) simply by an

UkusakazaL 2021-01-08 Answered
Let f be a function whose Maclaurin series expansion.
f(x)=3+12x+24x2+32x3+
Explain how you can determine f'(0), f''(0), and f'''(0) simply by analyzing the oefficients of x, x2, and x3 in the given representation and without directly alculating f'(x), f''(x), and f'''(x) from the representation above.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Nathanael Webber
Answered 2021-01-09 Author has 117 answers

A Macluarin series is a Taylor series expansion 0 a function about 0,
f(x)=f(0)+f(0)x+f(0)2!n2+f(0)3!n3+
Given that f(x)=3+12x+24x2+32x3+...
Comparing with the above definition we get f'(0)12,
f(0)26=24f(0)=48
f(0)3!=32f(0)=326=192
f'(0)=coefficient of xf(x)
f''(0)=2! x coefficient of x2f(x)
f'''(0)=3! x coefficient of x3f(x)

Not exactly what you’re looking for?
Ask My Question
Jeffrey Jordon
Answered 2021-11-07 Author has 2047 answers

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-11-23
Which of the following graphs represent functions that have inverse functions?
asked 2021-02-13
Find the principal of a 15-month loan with a rate of 6.5%, if it results in interest of $812.
asked 2021-11-17
Determine which functions are polynomial functions. For those that are, identify the degree.
f(x)=(x2+7)x3
asked 2020-12-24
Find the critical points of the following functions.Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical points.
f(x,y)=yexey
asked 2021-11-23
Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.
G(x)=3x2(x+2)3
asked 2021-10-11
Explain the difference between an absolute minimum and a local minimum.
a) There is no difference.
b) A function f has an absolute minimum at x=c if f(c) is the smallest function value on the entire domain.
c) A function f has an absolute minimum at x=c if f(c) is the smallest function value when x is near c, whereas f has a local minimum at c if f(c) is the smallest function value on the entire domain of f.
d) A function f has an absolute minimum at x=c if f(c) is the largest function value on the entire domain of f, whereas f has a local minimum at c if f(c) is the largest function value when x is near c.
e) A function f has an absolute minimum at x=c if f(c) is the largest function value when x is near c, whereas f has a local minimum at c if f(c) is the largest function value on the entire domain of f.
asked 2021-11-25
How are the sine and cosine functions related to the other four trigonometric functions?