The linear approximation for the function f(x)=x^5 near x=2 is 32+80(x-2) Check this.

A.) What number c will give the best quadratic approximation x^5 approximate to 32+80(x-2)+c(x-2)^2. With the help of myininaya I got c=80.

B.)If this approximation is used for various x's in the interval [2,2.1], can you be certian that the error is no bigger than .05? Explain using Taylor's inequality (the Error Bound).

C.) Graph part equation Part A now that we have c. On interval [2,2.1]. note: I don't need someone to graph this, I just want to make sure I have right approach. Would i just pick values for x on interval and set equation equal to y and solve?

Question

The linear approximation for the function f(x)=x^5 near x=2 is 32+80(x-2) Check this.

A.) What number c will give the best quadratic approximation x^5 approximate to 32+80(x-2)+c(x-2)^2.  With the help of myininaya I got c=80.

B.)If this approximation is used for various x's in the interval [2,2.1], can you be certian that the error is no bigger than .05?  Explain using Taylor's inequality (the Error Bound).

C.) Graph part equation Part A now that we have c. On interval [2,2.1].  note: I don't need someone to graph this, I just want to make sure I have right approach.  Would i just pick values for x on interval and set equation equal to y and solve?