FUNCTION F(x)=x/root x+1 at x=0 A)F(0) B)find f\"(x) and f\"(0) C)What is Lo(x)?

A)F(0)=0 B) ddxf(x)= 1x?+1?x?2?(x?+1)2

ID: 3288958 • Letter: F

Question

FUNCTION F(x)=x/root x+1 at x=0

A)F(0)

B)find f"(x) and f"(0)

C)What is Lo(x)? show your work

D)Plot f(x) and L(x) on the same set of axes with the x-axis varying from ?10..10 and y-axis varying from ?5..5.

Does Lo(x) lie ABOVE or BELOW f(x)?

Does Lo(x) UNDER estimate or OVER estimate f(x) near x = 0?

h) Calculate the value of L0(x) at x = 0.03. (This is the approximate value of f(0.03).)

i) Calculate the actual value of f(0.03).

j) Calculate the error between the approximate and the actual value.

You have been estimating the value of f(x) at x = 0.03. By hand,

draw a vertical line through x = 0.03 on the last plot you created.

The error in using the linear approximation rather than the actual function is represented by the distance between

L(x) and f(x) along the line through x = 0.03. Circle this error and label it on your graph.

A)F(0)=0

ddxf(x)= 1x?+1?x?2?(x?+1)2

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