Question

Use differentials to approximate (26)^1/3

Answer 1

The given function is cube root of x
Give a number that has a whole number as a cube root and is close to 26...
27
27^(1/3) = 3
So we have
x1 = 27 y1= 3 (because the function is y= x^(1/3)
x2= 26 y2= ?
change in x = -1
Take the derivative of the function

y' = (1/(2 (cube root of x^2))) x'
we are looking for y'
sub x=27 and x'=-1 into the equation
1/(2 (27)^(2/3)) -1
-1/2(9)
y'=-1/18

Take that value then add it to 3
3- 1/18
3 - 0.06
=2.94 (answer)
If you input cube root of 26 in a calcu it would give 2.96 (close enough)