Taylor Polynomials and Series

Let P\left(x\right)=3x^2-5x^3+7x^4+3x^5 be the fifth-degree Taylor polynomial for the function f about x=0 . What is the value of f^{'''}\left(0\right) ?

The difference or derivative formula is developed based on ..

• the definition of differentiation

• the definition of limits

• the Taylor series

• the graph of the slope of a function