Question
Use the limit definition of differentiability to find the derivatives of the following functions:(a) $f(x)=x^{4}+3 x$(b) $f(x)=1 / x$
Step 1
The derivative of a function \( f(x) \) at a point \( x \) is given by the limit: \[ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \] Show more…
Show all steps
Your feedback will help us improve your experience
Dakarai Holcomb and 84 other 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
Consider the function f(x) = (2x - 3)(1 - 5x). Find f'(x) using the limit definition of derivative: f'(x) = lim (f(x+Δx)-f(x))/Δx. b) Evaluate f'(x) analytically.
Use the limit definition to find the derivative of the function. $$ f(x)=4 x+1 $$
Differentiation
The Derivative and the Slope of a Graph
Use the limit definition to find the derivative of the function. $$ f(x)=x^{2}-4 $$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD