A) If f ( x ) =7cos 2 ( x ),compute its differential df . df =7sin(2 x )( dx ) Approximate the change in f when x changes from x = / 6to x = / 6+...

A) If f(x) = 7 cos2(x), compute its differential df.

df = −7sin(2x)(dx)  

Approximate the change in f when x changes from x = π/6 to 

x = π/6+ 0.1.(Round your answer to three decimal places.)

Δf ≈ _____   

Approximate the relative change in f as x undergoes this change. (Round your answer to three decimal places.)

_____

B) If f(x) = x3 − 6x2 − 8, compute its differential df.

df =  ______

Approximate the change in f when x changes from x = 2 to x = 2.1.

Δf ≈ ______ 

Use this value of Δf to approximate f(2.1).

f(2.1) ≈ _____