3. [-/1 Points] DETAILS SCALCET9 2.8.032. Find the derivative of the function using the definition of derivative. g(x) = 1 / (4 + ?x) g'(x) = State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using interval notation.) 4. [-/1 Points] DETAILS SCALCET9 2.8.041. The graph of f is given. State the numbers at which f is not differentiable. (Enter your answers as a comma-separated list.)
Added by Brooke C.
Close
Step 1
Given g(x) = 1/4 + √x, we need to find g'(x). Using the definition of derivative, we have: g'(x) = lim(h->0) [g(x + h) - g(x)] / h = lim(h->0) [(1/4 + √(x + h)) - (1/4 + √x)] / h = lim(h->0) [√(x + h) - √x] / h = lim(h->0) [(√(x + h) - √x) * (√(x + h) + √x)] / Show more…
Show all steps
Your feedback will help us improve your experience
Kathleen Carty and 60 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
Hemraj K.
Avinash V.
Analyzing Functions from Derivatives Answer the following questions about the functions whose derivatives are given in Exercises $1-14$ : $$\begin{array}{l}{\text { a. What are the critical points of } f ?} \\ {\text { b. On what intervals is } f \text { increasing or decreasing? }} \\ {\text { c. At what points, if any, does } f \text { assume local maximum and }} \\ {\text { minimum values? }}\end{array}$$ $$f^{\prime}(x)=(x-1)(x+2)(x-3)$$
Applications of Derivatives
Monotonic Functions and the First Derivative Test
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD