Use the equation $f'(a) = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}$ to find $f'(2)$ for $f(x) = x^2 - 3$.
Added by Larry M.
Close
Step 1
Step 1: First, we need to find f^(')(a) using the given equation f^(')(a)=\lim_(h->0)(f(a+h)-f(a))/(h). Show more…
Show all steps
Your feedback will help us improve your experience
Dwijendra Rao and 83 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
use algebra to find the limit exactly. $$\lim _{h \rightarrow 0} \frac{(5+h)^{2}-5^{2}}{h}$$
Foundation for Calculus: Functions and Limits
Introduction to Limits and Continuity
Use an algebraic simplification to help find the limit, if it exists. $$ \lim _{h \rightarrow 0} \frac{(x+h)^{2}-x^{2}}{h} $$
Limits of Functions
Introduction to Limits
Use the balanced difference quotient formula, $$ f^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a+h)-f(a-h)}{2 h} $$ to compute $f^{\prime}(3)$ when $f(x)=x^{2}$. What do you find?
Introduction to the Derivative
The Derivative: Algebraic Viewpoint
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