201k views
3 votes
Find absolute max and min of f(x)=(x)/(x²+4),[-5,5]

1 Answer

5 votes

Final Answer:

The absolute maximum of f(x) = x/(x² + 4) on the interval [-5, 5] occurs at x = -5 with a maximum value of -5/21, and the absolute minimum occurs at x = 5 with a minimum value of 5/29.

Step-by-step explanation:

To find the critical points, we first take the derivative of f(x) with respect to x and set it equal to zero:

f'(x) = (1 - x²)/(x² + 4)^2

Setting f'(x) equal to zero gives us x = ±1, but only x = 1 is within the interval [-5, 5]. Now, we evaluate f(x) at the critical point x = 1 and the endpoints x = -5 and x = 5.

f(-5) = -5/21, f(1) = 1/5, f(5) = 5/29

Therefore, the absolute maximum occurs at x = -5 with a value of -5/21, and the absolute minimum occurs at x = 5 with a value of 5/29.

It's important to note that the critical point x = 1 is not within the interval [-5, 5], so it is not considered in this context.

User Shanyu
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories