To find the coefficient 'a' of the linear interpolating function P(x) = ax, we need to use the formula for linear interpolation:

P(x) = f(x0) + [(f(x1) - f(x0)) / (x1 - x0)] * (x - x0)

Given that f(x) = x^2, we can substitute x0 = 0 and x1 = 1 into the function to find f(x0) and f(x1):

f(x0) = (0)^2 = 0
f(x1) = (1)^2 = 1

Substituting these values into the formula for P(x) gives:

P(x) = 0 + [(1 - 0) / (1 - 0)] * (x - 0)
= x

Therefore, the coefficient 'a' of the linear interpolating function P(x) = ax is 1.

Question

To find the coefficient 'a' of the linear interpolating function P(x) = ax, we need to use the formula for linear interpolation:

P(x) = f(x0) + [(f(x1) - f(x0)) / (x1 - x0)] * (x - x0)

Given that f(x) = x^2, we can substitute x0 = 0 and x1 = 1 into the function to find f(x0) and f(x1):

f(x0) = (0)^2 = 0
f(x1) = (1)^2 = 1

Substituting these values into the formula for P(x) gives:

P(x) = 0 + [(1 - 0) / (1 - 0)] * (x - 0)
     = x

Therefore, the coefficient 'a' of the linear interpolating function P(x) = ax is 1.

Knowee AI · Accepted Answer

To find the coefficient 'a' of the linear interpolating function P(x) = ax, we need to use the formula for linear interpolation:

P(x) = f(x0) + [(f(x1) - f(x0)) / (x1 - x0)] * (x - x0)

Given that f(x) = x^2, we can substitute x0 = 0 and x1 = 1 into the function to find f(x0) and f(x1):

f(x0) = (0)^2 = 0
f(x1) = (1)^2 = 1

Substituting these values into the formula for P(x) gives:

P(x) = 0 + [(1 - 0) / (1 - 0)] * (x - 0)
     = x

Therefore, the coefficient 'a' of the linear interpolating function P(x) = ax is 1.

Consider the function given by f(x) = x^2. Determine the coefficient a of the linear interpolating function P(x) = ax that interpolates f at two nodes x0 = 0 and x1 = 1