2. Use the graph of f(x) below to answer the given questions. (a) ...

  1. Home
  2. Homework Library
  3. Mathematics
  4. Calculus
  5. 2. Use the graph of f(x) below to answer the given questions. (a) ...

QuestionQuestion

Transcribed TextTranscribed Text

2. Use the graph of f(x) below to answer the given questions. (a) Where f 0 (x) = 0 x = −3, x = 2 (b) Where f 0 (x) is undefined. x = −1, x = 5 (c) Find all local maximum and minimums of f(x) local Minimum at x = −3 local Max at x = 5 (d) Find all the absolute maximums and minimums of f(x) None 3. Using the graph and your answers to the previous question, do the following; label all the critical points on a number line, determine the sign of the derivative of x between each critical point. How does this information on the number line help you determine which critical points correspond to local maximums, minimums, or neither. 4. In each case, sketch a graph of a CONTINUOUS function with the given properties. (a) f 0 (−1) = 0 and f 0 (3) = 0 (b) g 0 (1) = 0and g 0 (4)is undefined (c) h 0 (−2) = 0and h 0 (2) = 0 and h 0 (0) is undefined 5. Use calculus to determine the (a) critical points, (b) local extrema, (a) intervals on which the function is increasing or decreasing. (a) f(x) = x 4 + 2x 3 − 1 f 0 (x) = 4x 3 + 6x 2 0 = 2x 2 (2x + 3) x = 0, x = −3/2 f 0 (x) -3/2 0 − + + Inc: (−3/2, 0) ∪ (0, ∞) Dec: (−∞, −3/2) Min (-3/2, -2.6875) 7. For the following functions find the open intervals on which the function is increasing and decreasing. Identify the functions local and absolute extreme values, if any, saying where they occur. (a) f(x) = e √ x f 0 (x) = e √ x x √ x 0 = e √ x x √ x x = 0 f(0) = 1 Absolute Min f 0 (x) 0 DNE + (b) f(x) = x 2 ln(x) f 0 (x) = 2x ln(x) + x 0 = x(2 ln(x) + 1) x = 0, x = e −1/2 f(0) = DNE, f(e −1/2 = −.18394)AB and Local Min f 0 (x) 0 e −1/2 − + (c) f(x) = x 2/3 (x + 5) f 0 (x) = x 5/3 + 5x 2/3 0 = 5x + 10 3x 1/3 x = 0, x = −2, f(0) = 0Min, f(−2) ≈ 4.762203 Max f 0 (x) −2 0 + − + 8. Sketch the graph of the differential function y = f(x) through the point (1, 1) if f 0 (1) = 0 and f 0 (x) > 0 for x > 1 and f 0 (x) < 0 for x < 1 9. Given the graph of f 0 below, find the following. Then sketch the graph of f if f is continuous and f(−6) = 0 (a) The intervals where f is increasing and decreasing. (b) The x values of any local extrema (c) The end behavior of the graph.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution.pdf.

    $33.00
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Calculus Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats