calculus problem?

Question

hi i need some explanation to this problem
1. Find the tangent line approximation to f(x) x^2/3 at x=8

2. use your answers to number 1 to obtain a linear approximation estimating the value of (7.98)^2/3

3 will this be an overestimate or an underestimate

Answer 1

1. (If you mean x^(2/3))
The slope will be: f'(x) = 2/(3x^(1/3)); f(8) = 1/3
So if the line goes through (8, 4):
y - 3 = (1/3)(x-8)
y = x/3 + 4/3

2. 798/300 + 400/300 = 1198/400 = 5.99/2 = 2.995

3. It will be over.