Finding Position from Velocity or Acceleration
Exercises 45–48 give the acceleration a=d²s/dt², initial velocity, and initial position of an object moving on a coordinate line. Find the object’s position at time t.
a = 9.8, v(0) = −3, s(0) = 0
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
