Use linear approximation, i.e. the tangent line, to approximate √16.4 as follows:Let f(x)=√x. Find the equation of the tangent line to f(x) at x=16 L(x) =

Question

Use linear approximation, i.e. the tangent line, to approximate  as follows:Let . Find the equation of the tangent line to  at  =   

Using this, we find our approximation for  is  NOTE: For this part, give your answer to at least 9 significant figures or use an expression to give the exact answer.

Answer 1

f(x) = √x; f'(x) = 1/(2√x); x = 16; f(16) = √16 = 4; f'(16) = 1/(2√16) = 1/8;

Equation of tangent line at point (16, 4): y = 4 + 1/8(x - 16); y = 1/8x + 2

L(x) = 1/8x + 2; f(16.4) ≈ 1/8·16.4 + 2 = 4.05