Question

How do you find the linearization at a=1 of `f(x)=x^(3/4)`?

Answer 1

It is the equation of the tangent line at `(1,f(1))`

Explanation:

`f(x) = x¾`

`f(1) - 1^(3/4) = 1`

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

The tangent line has point-slope equation
`y-1 = 3/4(x-1)`,

so the linearization is

`L(x) = 1 + 3/4(x-1)`