Question

Using the Horner’s method find the values of f(4) and f' (4) for the polynomial
f(x) = x⁴ + 2x³ - x² + 1

Answer 1

Solution. To calculate the value of the function by Horner's method, we use the algorithm.

Let

$$f(x)=a_0x^n+a_1x^{n-1}+...+a_{n-1}x+a_n$$

а) p=0

b) for i=1 to n do p=p*x+a_i

$$f(x)=p$$

Сreate a table for calculating the value of the function by Horner's method x=4

As result

$$f(4)=369$$

Find the first derivative of the function f(x).

$$f'(x)=4x^3+6x^2-2x$$

To calculate the value of the function by Horner's method, we use the algorithm for x=4.

As result

$$f'(4)=344$$

Answer.

$$f(4)=369$$ $$f'(4)=344$$