`g(x) = |x + 4|, [-7,1]` Find the absolute extrema of the function on the closed interval.

Textbook Question

Chapter 3, 3.1 - Problem 30 - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

shumbm's profile pic

Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

Hello!

For x<=-4  x+4<=0 and g(x) = -(x+4).
The minimum on the interval [-7, -4] is at the x=-4, g(-4) = 0.
The maximum on the interval [-7, -4] is at the x=-7, g(-7) = 3.

For x>=-4  x+4>=0 and g(x) = (x+4).
The minimum on the interval [-4, 1] is at the x=-4, g(-4) = 0.
The maximum on the interval [-4, 1] is at the x=1, g(1) = 5.

Therefore the global minimum of g on [-7, 1] is 0 at x=-4 and
the global maximum of g on [-7, 1] is 5 at x=1.

We’ve answered 318,916 questions. We can answer yours, too.

Ask a question