Approximation based on linearization

Question

Approximate 15^1/4 using the Linear Approximation L(x) of f(x) = x^1/4 at a = 16.

(Use symbolic notation and fractions where needed.)

approximation based on linearization:

Answer 1

L(x) = f(a) + f'(a) (x-a)

a = 16

f(a) = 16^1/4 = 2

f'(x) = 1/4 x ^-3/4 so f'(2) = 1/4 ( 2^-3/4)

So L(x) = 2 + 1/4 (2^-3/4) (x-16)

Now you can find L (15)