HW 5.4.2: The Derivative and Function Information Use your knowledge of derivatives to answer the questions. A calculator should not be used. 1. Given fix) =13x2 +SIx+1 answer the following: a. Is the function increasing or decreasing at x: 2 '? in. List the intervalis] on which x] is increasing. c. List the intervalis) on which for.) is decreasing. d. At what value{s} does for.) have a relative maximum or minimum? e. {Optional} Sketch what you think the graph of x) should look like based on your answers from h-d. 2. Given f(x)=3x112x+7 answer the following: a. Is the function increasing or decreasing at x: 3 '? in. List the intervalis) on which f{x} is increasing. c. List the intervalis] on which x} is decreasing. d. At what value{s} does f{.x} have a relative maximum or minimum? e. {Optional} Sketch what you think the graph of x} should look like based on your answers from h-d. 3. Given x) = :c3 + 31-" + 24x 5 answer the following: a. Is the function increasing or decreasing at x: 3 '? in. List the intervalis) on which f{x} is increasing. c. List the intervalis) on which f{x} is decreasing. d. At what value{s} does f{.x} have a relative maximum or minimum? e. {Optional} Sketch what you think the graph of x} should look like based on your answers from h-d. 4. Given f(x)=-2x' +15x -6 answer the following: a. Is the function increasing or decreasing at x=-1? b. List the interval(s) on which f(x) is increasing. C. List the interval(s) on which f(x) is decreasing. d. At what value(s) does f(x) have a relative maximum or minimum? e. (Optional) Sketch what you think the graph of f(x) should look like based on your answers from b-d. 5. Given f(x) = x* -8x' +3 answer the following: a. Is the function increasing or decreasing at x=-1? b. List the interval(s) on which f(x) is increasing. C. List the interval(s) on which f(x) is decreasing. d. At what value(s) does f(x) have a relative maximum or minimum? e. (Optional) Sketch what you think the graph of f(x) should look like based on your answers from b-d