Mat 270: Calc 3.10

Question

I want to preface this by asking for an example with the same structure as the problem I provide so I can solve it. Such as giving an example of 8x+3=15 instead of my given 4x+12=32

The question I need help on:

Use linear approximation, i.e the tangent line, to approximate 1/0.503 as follows

Let f(x) =1/x and find the equation of the tangent line in slope-intercept form to f(x) at a "nice" point near 0.503

Then use the approximate 1/0.503

Answer 1

f(x) = √x

Approximate √4.02

√4.02 = f(4.02) ≈ L(4.02) = f(4) + f'(4)(4.02 - 4)