Section 3.1 Day 2 Extrema on an Interval Class Quiz AP Calculus AB

Problem 1 Find the extreme values of 𝑓 𝑥 = 5−2 𝑥 2 , 𝑥≤1 𝑥+2, 𝑥>1 on the interval [−1, 2]

Problem 2 The velocity of a particle is moving on the x-axis is given by 𝑣 𝑡 = 𝑡 3 −6 𝑡 2 for the time 0≤𝑡≤10 A) When is the particle farthest to the left? B) When is the velocity of the particle increasing the fastest?

Problem 3 Find the extreme values of 𝑓 𝑥 = 𝑥 2 3 on the interval [−2, 3] Min (0, 0) Max 3, 3 9

Problem 4 Find the extreme values for 𝑓 𝑥 =ln⁡(𝑥+1) on the interval [0, 3] Min: (0, 0) Max: (3, ln 4 )

Problem 5 Find the extreme values for 𝑓 𝑥 = 𝑒 −𝑥 on the interval [−1, 1] Min: (1, −𝑒) Max: −1, − 1 𝑒