The straight line through (1, 2) and (3, 8) interpolates the data. What value does it give at x equal 2?

Answer: ______________

Three data points have distinct x values zero, one and two. What is the largest degree the interpolating polynomial can have?

• 1
• 3
• 2
• 4

Three data points have distinct x values 0, 1 and 2. What is the largest degree the interpolating polynomial can have?

• 1
• 2
• 3

Using more and more equally spaced points always makes the worst interpolation error smaller.

Circle one:   True   False

Which formula gives the linear interpolation error at distinct nodes x0 and x1?

• f(x) - p(x) = f''(xi) / 2 times (x - x0)(x - x1)
• f(x) - p(x) = f''(xi) times (x - x0) + (x - x1)
• f(x) - p(x) = f'(xi) times (x - x0)(x - x1)

For distinct nodes x0 and x1, which formula gives the linear interpolation error?

• f prime of xi times (x minus x0) times (x minus x1)
• f(x) minus p(x) equals f double prime of xi times (x minus x0) plus (x minus x1)
• f(x) minus p(x) equals f double prime of xi times (x minus x0) times (x minus x1)
• f(x) minus p(x) equals f double prime of xi divided by 2 times (x minus x0) times (x minus x1)

For the data points (0, 1) and (2, 9), what is the first divided difference of f over these nodes?

• 4
• 5
• 8
• 10

For the points (0, 1) and (2, 9), what is the first divided difference?

• 2
• 4
• 8

With nodes 0, 1 and 2, the first Lagrange basis piece is (x - 1)(x - 2) / 2. What is its value at x = 0.5?

Answer: ______________

Two different polynomials, each of degree at most 2, pass through the same three points with distinct x coordinates. Is that possible?

Circle one:   True   False