Question

1. y = 2x³ - 3x + 1 [-2,2]

2. y = 7 - x² [-1,2]

3. y = e^x [0,ln4]

for each of the following 1-3, is the instantaneous rate of change equal to the average rate of change? If so, where?

4. for each of the following a-c,  find the critical points, determine if there is an absolute max and or min, if so, find them

a. y = 2x³ - 15x² + 24x [0,5]

b. y = x / (x²+3)² on [-2,2]

c. (4x³ / 3 ) + 5x² - 6x on [-4,1]

Answer 1

In question 4, as we are finding absolute Maxima and minima, we need not perform the double derivative test. The double derivative test only helps us to find local maximum and minimum. Directly evaluating and computing values of function at critical points and comparing the values yields absolute Maxima and minima