Lt f be the functin given by f(x)=2x^3. If the values in the table are used to estimate f'(0.5), what is the difference between the estimation and the actual value of f'(0.5)?

Question

X : 0 1

f(x): 1 2

Lt f be the functin given by f(x)=2^{x^3}. If the values in the table are used to estimate f'(0.5), what is the difference between the estimation and the actual value of f'(0.5)?

A) 0

B) 0.433

C) 0.567

D) 1

-the numbers above are supposed to be in table format such as 0 and 1 being with x and 1 and 2 beng with f(x)

Answer 1

f(x) = 2^{x^3}

f ' (x) = 3ln(2)x²⋅2^{x^3}

f ' (0.5) = 3ln(2)(0.5)²⋅2^{0.5^3}=0.567

Approximating using the table:

f ' (0.5) = (y2-y1)/(x2-x1) = (2-1)/(1-0) = 1

The difference = 1 - 0.567 = 0.433

So, the answer is B)