Consider the interpolating polynomial for f(x) = 15 with interpolation nodes x = 0, 2, 4, 6, 8, 10. x+5 (a) Find an upper bound for the interpolation error at x = 1. (b) Find an upper bound for the interpolation error at x = 5. (c) Find an upper bound for the interpolation error for 0 < x < 10.

The difference quotient is defined as f(x+h)={(x) where h + 0. Find m for f(x) = x² – 9

Use the intermediate value theorem to show that function has a zero between the two numbers given. Then, use your calculator to approximate the zero to the nearest hundredth. P(x)=8x^4 - 8x^2 + 20x -16; 0.5 and 1 (a) evaluate the function for the lower bound, 0.5 P(0.5)= ? (b) evaluate the function for the upper bound, 1 P(1)= ? Why do P(0.5) and P(1) show that the function has a zero between 0.5 and 1? Multiple choice A. Since P(0.5) and P(1) have the same sign, there exists at least one real zero between 0.5 and 1. B. Since P(0.5) # P(1), there exists at least one real zero between 0.5 and 1 C. Since P(0.5) < P(1), there exists at least one real zero between 0.5 and 1. D. Since P(0.5) and P(1) are opposite in sign, there exists at least one real zero between 0.5 and 1.