Finding Indefinite Integrals
In Exercises 17–56, find the most general antiderivative or indefinite integral. You may need to try a solution and then adjust your guess. Check your answers by differentiation.
∫(cscθ cotθ) / 2 dθ
Finding Critical Points
In Exercises 41–50, determine all critical points and all domain endpoints for each function.
y = x − 3x²ᐟ³
Roots (Zeros)
Show that the functions in Exercises 19–26 have exactly one zero in the given interval.
f(x) = x³ + 4x² + 7, (−∞, 0)
Checking Antiderivative Formulas
Verify the formulas in Exercises 57–62 by differentiation.
∫(3x + 5)⁻² dx = −(3x + 5)⁻¹/3 + C
Roots (Zeros)
Show that the functions in Exercises 19–26 have exactly one zero in the given interval.
f(x) = x⁴ + 3x + 1, [−2, −1]
Absolute Extrema on Finite Closed Intervals
In Exercises 21–36, find the absolute maximum and minimum values of each function on the given interval. Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates.
h(x) = ³√x, −1 ≤ x ≤ 8
