Question

Given the function f(x)= 2^x, which of the following best represents the value of the numerical derivative f prime 5, determined using the symmetric difference quotient with h=0.5

Answer 1

The value of the numerical derivative fprime(5) of the function f(x) = 2^x using the symmetric difference quotient with h=0.5 is approximately 2.13.

Step-by-step explanation:

The question asks us to find the numerical derivative fprime(5) of the function f(x) = 2^x using the symmetric difference quotient with h=0.5. The symmetric difference quotient is given by the formula:

fprime(x) = (f(x+h) - f(x-h)) / (2h)

Substituting the values into the formula, we have:

fprime(5) = (2^(5+0.5) - 2^(5-0.5)) / (2*0.5)

= (2^5.5 - 2^4.5) / 1

= approximately 2.13