Question

The derivative of a continuous function is
f′(x) = 2x(x − 1)^3
Find the open intervals on which f is increasing
A)None of these
B)On (−∞, 0) and on (1, ∞)
C) On (−∞, 0)
D) On (0, 1)
E) On (−1, 0)

Answer 1

increasing and decreasing - first derivative
concave up concave down - second derivative
you need to graph the function and determine where it is increasing

Answer 2

f′(x) = 2x(x − 1)^3
If f'(x) > 0 in an interval, f(x) is increasing in that interval.
When is f′(x) = 2x(x − 1)^3 > 0 ?

Answer 3

first we need to find all values of x that equal to 0.
then we create a sign chart
so the equation is 0 when x = 0 and 1
so pick any point within those areas