# 4.3

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1. Consider the equation below. F(x) = 2x^3+3x^2-336x. Find the interval on which f is decreasing.(Enter your answer in interval notation.) Find the local minimum and maximum values of f. Find the inflection point. Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down.(Enter your answer in interval notation.)
2. Consider the equation below. F(x) 4x^3 + 21x^2 – 294x + 4. Find the interval on which f is decreasing.(Enter your answer in interval notation.) Find the local minimum and maximum values of f. Find the inflection point. Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down.(Enter your answer in interval notation.)
3. Consider the equation below. F(x) = 5 sin x + 5 cos x, 0<= x <= 2pi. Find the interval on which f is decreasing.(Enter your answer in interval notation.) Find the local minimum and maximum values of f. Find the inflection point. Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down.(Enter your answer in interval notation.)
4. Consider the equation below. f(x) = 8 cos^2x – 16 sin x, 0<= x <= 2piFind the interval on which f is decreasing.(Enter your answer in interval notation.) Find the local minimum and maximum values of f. Find the inflection point. Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down.(Enter your answer in interval notation.)
5. Consider the equation below. F(x) = e^2x + e^-x. Find the interval on which f is decreasing.(Enter your answer in interval notation.) Find the local minimum and maximum values of f. Find the inflection point. Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down.(Enter your answer in interval notation.)
6. Consider the equation below. F(x)= x^5 ln x. Find the interval on which f is decreasing.(Enter your answer in interval notation.) Find the local minimum and maximum values of f. Find the inflection point. Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down.(Enter your answer in interval notation.)
7. Find the local maximum and minimum values of f using both First and second derivative test.
f(x) = 3 + 9x^2 -6x^3
8. Consider the equation below. F(x) = 7 + 2x^2 – x^4. Find the interval on which f is decreasing.(Enter your answer in interval notation.) Find the local minimum and maximum values of f. Find the inflection point. Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down.(Enter your answer in interval notation.)
9. Consider the equation below. F(x) = 170 + 8x^3 + x^4 . Find the interval on which f is decreasing.(Enter your answer in interval notation.) Find the local minimum and maximum values of f. Find the inflection point. Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down.(Enter your answer in interval notation.)
10. Consider the equation below. F(x) = ln(x^4 + 27). Find the interval on which f is decreasing.(Enter your answer in interval notation.) Find the local minimum and maximum values of f. Find the inflection point. Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down.(Enter your answer in interval notation.)
11. Consider the equation below. F(x) = 1 + 5/x – 9/x^2. Find the interval on which f is decreasing.(Enter your answer in interval notation.) Find the local minimum and maximum values of f. Find the inflection point. Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down. (Enter your answer in interval notation.)
12. Suppose the derivative of a function f is f’(x) = (x+1)^4 (x-2)^7 (x-7)^6. On what interval is f increasing? (Enter your answer in interval notation.)
13. Consider the function below. f(x) = x^2 e^-x
Find the exact value of the minimum of f for x >= 0.
14. Find a cubic function f(x) = ax^3 + bx^2 + cx + d that has local maximum value of 4 at x = -2 and a local minimum value of 0 at x = 1.
15. Consider the function below.
f(x) = x^2/ x^2 -16
(a) Find the vertical and horizontal asymptotes.
(b) Find the interval where the function is increasing. (Enter your answer using interval notation.) Find the interval where the function is decreasing.
(c) Find the local maximum value.
(d) Find the interval where the function is concave up.
(e) Find the interval where the function is concave down.