help? I have a few questions oreview sheet that i need help with .

Question

anonymous · Answer

Use a tangent line approximation with the function $$g(x)=\sqrt{x}$$ to estimate $$\sqrt{9.2}$$

mathmale · Answer

A typical equation for a straight or tangent line approximation to a function f(x) at x-value a is L(x) = f(a) + f'(a)*(x-a).

Here the starting value is 9 (because the square root of 9 is so easily found).  That means (x-a) will become 9.2 - 9, or 0.2.

Find the derivative dg/dx and let x = 9.
Evaluate g(x) at x = 9.

Put this all together:  L(9.2) = f(9) + f'(9) * (9.2 - 9)  =  ??

anonymous · Answer

whats the first derivative of 9?

anonymous · Answer

f'(9) does not mean the derivative of 9, but the derivative of f(x) evaluated at 9.

mathmale · Answer

Example:  if g(x) = Sqrt(x) (as is true in this math problem), the derivative g'(x) is 1/(2*Sqrt(x)).  To evaluate g'(9), replace x by 9:  1/(2*Sqrt(9)).  Value?