Math Problem Statement

Use calculus to find the absolute maximum and minimum values of the function.

f(x) = 3x − 6 cos x,    −2 ≤ x ≤ 0

(a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.

maximum

minimum

(b) Use calculus to find the exact maximum and minimum values.

maximum

(7π/6,4.29)

minimum

(−2,−12.39)

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Trigonometric Functions
Maxima and Minima

Formulas

f'(x) = 3 + 6sin(x)
f(x) = 3x - 6cos(x)
Critical points: Set f'(x) = 0

Theorems

First Derivative Test
Cosine Function Properties

Suitable Grade Level

Grades 11-12 (Calculus)