### Graphing Transformation

### Lesson 5: Derivative

(A) Introduction

y = f '(x)

This transformation involves the values of the gradient of the original graph of y = f (x) as x varies.

(B) Transformation of features

y = f (x)

(I)

Vertical asymptote x = k

(II)

Horizontal asymptote y = b

(III)

Oblique asymptote y = mx + c

y = f '(x)

Vertical asymptote x = k

Horizontal asymptote y = 0

Horizontal asymptote y = m

(IV)

Stationary point (a, b)

(V)

f (x) is increasing

(VI)

f (x) is decreasing

(VII)

f (x) concave upwards

(VIII)

f (x) concave downwards

x intercept (a, 0)

f '(x) > 0

f '(x) < 0

f '(x) increasing

f '(x) decreasing

Example 1

Given the following graph of y = f (x), sketch the graph of y = f '(x).

Solution

Example 2

Given the following graph of y = f (x), sketch the graph of y = f '(x).

Solution