linear approximation

Question

Find the local linear approximation of the function  at , and use it to approximate  and .

(a)  

(b)  

(c)  

For parts (b) and (c), you should enter your answer as a fraction. If you enter a decimal, make sure that it is correct to at least six decimal places.

Answer 1

(a) x = 5; f(5) = √(11 + 5) = 4; f'(x) = 1/[2√11 + x)]; f'(5) = 1/8

L(x) = 4 + 1/8(x - 5) = 1/8x + 27/8

(b) f(15.9) = L(4.9) = 1/8·( 4.9) + 27/8 = 3.9875

(c) f( 16.1) ≈ L(5.1) = 1/8·5.1 + 27/8 = 4.0125