Maxima and Minima Worksheet

Solutions

Calculate the Maximums and Minimums of the Following Functions:

1 f(x) = x3 − 3x + 2

2 Maxima and Minima Exercise

3 Maxima and Minima Exercise

4 Maxima and Minima Exercise

5 Maxima and Minima Exercise

6 Maxima and Minima Exercise

7 Maxima and Minima Exercise


1

f(x) = x3 − 3x + 2

f'(x) = 3x2 − 3 = 0

f''(x) = 6x

f''(−1) = −6 Maximum

f''(1) = 6 Minimum

f(−1) = (−1)3 − 3(−1) + 2 = 4

f(1) = (1)3 − 3(1) + 2 = 0

Maximum(−1, 4) Minimum(1, 0)


2

Maxima and Minima Exercise

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Solution

Solution


3

Maxima and Minima Exercise

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Solution

Solution

Solution


4

Maxima and Minima Exercise

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Solution


5

Maxima and Minima Exercise

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Solution

Solution

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6

Maxima and Minima Exercise

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Solution


7

Maxima and Minima Exercise

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Maxima and Minima Operations

Solution

Solution

Solution