(a) Let f (x) = ln x . Use intervals of size 0.1 to estimate f' (1) , f' (2) , f' (3) , f' (4) ,...

Question:

(a) Let f (x) = ln x . Use intervals of size 0.1 to estimate f' (1) , f' (2) , f' (3) , f' (4) , and f' (5). Use x = 1 , x = 2 , x = 3 , x = 4 , and x = 5 as the starting points for the intervals. Round your answers to two decimal places.

(b) Use your answers to part (a) to guess a formula for the derivative of f (x) = ln x .

Finite Difference:

The first derivative of a function f(x) at a point x can be approximated as the the ratio between the variation of function values to the

variation of the independent variable x, that is

{eq}D = \frac{ f(x+h) - f(x) }{ h} {/eq}

Answer and Explanation:

We consider the function

{eq}f (x) = \ln x {/eq}

a) The derivative of the function at points x = 1 , x = 2 , x = 3 , x = 4 , and x = 5 using an...

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Derivatives: The Formal Definition

from Math 104: Calculus

Chapter 8 / Lesson 5
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