Consider the equation below:
1. f(x) =2x^3 + 3x^2 - 72x
2. f(x) = 4x^3 + 21x^2 - 294x + 3
3. f(x) = 7 + 2x^2 - x^4
4. f(x) = 5 sin(x) + 5 cos(x), ( 0
less than or equal to x less than or equal to 2 pie )
5. f(x) = x^3 - x^2 -12x + 4,
[0, 4]
Find:
a. the interval on which f is increasing
b. the interval on which f is decreasing
c. the local minimum values of f
d. the local maximum value of f
e. the inflection points:
(x,y)
= ........................(smaller x-value)
(x,y)
= ........................(larger x-value)
f. the interval on which f is concave up
g. the interval on which f is concave down
i. the inflection points
j. sketch a graph of the function for each equation above