Find the maximum and minimum values attained by the function on the interval [0, 2].
The equation has three distinct real roots. Approximate
their locations by evaluating f at -2, -1, 0, 1, and 2. Then use Newton's
method to approximate each of the three roots to four-place accuracy
f(x)= x^3- 3x+ 1
Sand falling from a hopper at forms a conical sand pile whose radius is always equal to its height. How fast is the radius increasing when the radius is 5ft?
Find the open intervals on the x-axis on which the function is increasing and those on which it is decreasing.
This shows how to work with functions and roots, rate of change, and values.