Absolute Extrema on Finite Closed Intervals


In Exercises 37–40, find the function’s absolute maximum and minimum values and say where they occur.


f(x) = x⁴ᐟ³, −1 ≤ x ≤ 8

Finding Extreme Values

In Exercises 1–10, find the extreme values (absolute and local) of the function over its natural domain, and where they occur.

y = 𝓍³ ― 2𝓍 + 4

In Exercises 9–66, graph the function using appropriate methods from the graphing procedures presented just before Example 9, identifying the coordinates of any local extreme points and inflection points. Then find coordinates of absolute extreme points, if any.

53. y = x * √(8 - x²)

Finding Critical Points

In Exercises 41–50, determine all critical points and all domain endpoints for each function.

y = x² + 2/x

"Roots (Zeros) Show that the functions in Exercises 19–26 have exactly one zero

Solve the initial value problems in Exercises 71–90.

y⁽⁴⁾ = −sin t + cos t;

y′′′(0) =7, y′′(0) = y′(0) = −1, y(0) = 0

Business and Economics

60. Production level Prove that the production level (if any) at which average cost is smallest is a level at which the average cost equals marginal cost.