Find the quadratic polynomial g(x)-ax^{2} + bx + c text{which best fits the function} f(x)=e^{x} text{at} x=0, text{in the sense that} g(0)=f(0), text{and} g'(0)=f'(0), text{and} g''(0)=f''(0). Using a computer or calculator, sketch graphs of f and g on the same axes. What do you notice?

aflacatn 2021-01-30 Answered
Find the quadratic polynomial g(x)ax2 + bx + c which best fits the function f(x)=ex at x=0, in the sense that g(0)=f(0), and g(0)=f(0), and g(0)=f(0). Using a computer or calculator, sketch graphs of f and g on the same axes. What do you notice?
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

delilnaT
Answered 2021-01-31 Author has 94 answers

Step 1 The functions f(x) and g(x) are: f(x)=ex
g(x)=ax2 + bx + c
f(x)= d(f(x))dx= d(ex)dx

Using formula for derivative of exponential function: f(x)=ex
f(x)= d(f,(x))dx= d(ex)dx

Using formula for derivative of exponential function: f(x)=ex
g(x)= d(g(x))dx= d(ax2 + bx + c)dx

Using Theorem 3.2: g(x)= d(ax2)dx + d(bx)dx + d(c)dx

Using Theorem 3.1: g(x)=a × d(x2)dx + b × d(x)dx + 0

Step 2 Using Power Law: g(x)=a × 2 × x2  1 + b × 1 + 0
g(x)=2ax + b
g(x)= d(g(x))dx= d(2ax + b)dx

Using Theorem 3.2: g(x)= d(2ax)dx + d(b)dx

Using Theorem 3.1:

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

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