Recall that linear approximation to the function f(x) at a is given by L(x)= f(a)+f'(a)(x-a)
1. Setting f(x)=x^4 and a=2 give an estimate of (1.999)4.
2. A quadratic approximation is given by Q(x)=f(a)+f'(a)(x-a)+1/2 f''(a)(x-a)^2. Use this formula to approximate (1.999)^4.
3. Use a calculator to determine the true value of (1.999)^4. Which approximation was better, the linear or quadratic?
4. Guess a formula for a cubic approximation.

Question

Recall that linear approximation to the function f(x) at a is given by L(x)= f(a)+f'(a)(x-a)
1. Setting f(x)=x^4 and a=2 give an estimate of (1.999)4.
2. A quadratic approximation is given by Q(x)=f(a)+f'(a)(x-a)+1/2 f''(a)(x-a)^2. Use this formula to approximate (1.999)^4.
3. Use a calculator to determine the true value of (1.999)^4. Which approximation was better, the linear or quadratic?
4. Guess a formula for a cubic approximation.