The graph of f ′′(x) is continuous and decreasing with an x-intercept at x = −3. Which of the following statements must be true? The graph of f is always concave down. The graph of f has an inflection point at x = –3. The graph of f has a relative minimum at x = –3. None of these is true.
Added by J M.
Step 1
This means that for x < -3, f''(x) > 0 (concave up) and for x > -3, f''(x) < 0 (concave down). Show more…
Show all steps
Close
Your feedback will help us improve your experience
Ma. Theresa Alin and 82 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The graph of f'(x) is continuous and decreasing with an x-intercept at x = -3. Which of the following statements must be true? 1. The graph of f is always concave up. 2. The graph of f has an inflection point at x = -3. 3. The graph of f has a relative minimum at x = 4. 4. None of these is true.
Matthew E.
The graph of f', the derivative of the function f, is shown below. Which of the following statements must be true? I. f has a relative minimum at x = -3. II. The graph of f has a point of inflection at x = -2. III. The graph of f is concave down for 0 < x < 4 a. I only b. II only c. III only d. I and III only e. I and II only Graph of f'
Khushbu R.
The graph of f'(x) is continuous, positive, and has a relative maximum at x = 0. Which of the following statements must be true? The graph of f is always concave down. The graph of f is always increasing. The graph of f has a relative maximum at x = 0. The graph of f has a relative minimum at x = 0.
Andrew N.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD