FINDING ABSOLUTE MAXIMUM AND MINIMUM ON A CLOSED INTERVAL WORKSHEET

For each problem, find all points of absolute minima and maxima on the given closed interval.

Problem 1 :

y = −x³ − 6x² − 9x + 3; [−3, −1]

Problem 2 :

Problem 3 :

f(x) = x³ + 6x² + 9 x + 3 ; [-4, 0]

Problem 4 :

f(x) = x⁴ - 3x²+ 4; [-1, 1]

Problem 5 :

Answer Key

1)  So, absolute minimum is at (-3, 3) and absolute maximum is at (-1, 7).

2)  So, absolute minimum is at (5, 8/29) and absolute maximum is at (0, 2).

3)  

Absolute maxima are at (0, 3) and (-3, 3)

Absolute minimum are at (-4, 1) and (-1, 19)

4)  

Absolute minima are at (-1, 2) and (1, 2).

Absolute maximum is at (0, 4).

5)