Use differential, (i.e. linear approximation), to approximate cube root of 64.1 as follows:

Question

Let f(x) = cube root of x. The linear approximation to f(x) at x = 64 can be written in the form y = mx+b. Compute m and b and find cube root of 64.2 via linear approximation

Answer 1

dy = 1/3 x^-2/3 dx
At x=4, dy = 1/48 dx
So, use dx=0.2 to find dy, and add that to y(64)=4

Note also that since the slope is 1/48,

y-4 = 1/48 (x-64)