Question

Given the function f(x) = 2^x, which of the following best represents the value of the numerical derivative f' (5),

determined using the symmetric difference quotient with h = 0.5?
|
22.181
22.198
22.627
26.510
30.000

Answer 1

The numerical derivative of the function f(x) = 2^x at x = 5 using the symmetric difference quotient with h = 0.5 is approximately 22.181.

Step-by-step explanation:

The student is asking to compute the numerical derivative of the function f(x) = 2^x at x = 5 using the symmetric difference quotient with h = 0.5.

To find the numerical derivative, also known as the approximate derivative, we use the formula: f'(x) ≈ [f(x + h) - f(x - h)] / (2h). Plugging the values into the equation, we get:

f'(5) ≈ [f(5.5) - f(4.5)] / (2*0.5)

Now we calculate f(5.5) = 2^5.5 and

f(4.5) = 2^4.5, then plug these values back into the symmetric difference quotient:

f'(5) ≈ [2^5.5 - 2^4.5] / 1

After performing the calculations, we find that the closest answer to our computed value is 22.181, which is an approximation of the derivative of f(x) at x = 5 using the given method.