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07:09
06:02In 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
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
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.
Roots (Zeros)
Show that the functions in Exercises 19–26 have exactly one zero in the given interval.
g(t) = √t + √(1 + t) − 4, (0, ∞)
