how do i do this math problem?
use the defintion f^1(a) = lim as h heads toward 0 {f(x)-f(a)} / (x-a)
To solve this math problem, you are given the definition of the derivative. Let's break it down step by step.
The notation "f^1(a)" represents the derivative of function f at point a. It is also denoted as f'(a) or dy/dx(a).
The definition of the derivative is given as:
f^1(a) = lim(h->0) [f(x) - f(a)] / (x - a)
Here's how you can apply this definition to find the derivative of a function at a specific point:
1. Identify the function for which you want to find the derivative.
2. Substitute the function f(x) and the point a into the derivative definition:
f^1(a) = lim(h->0) [f(x) - f(a)] / (x - a)
3. Simplify the equation by replacing all instances of x with a:
f^1(a) = lim(h->0) [f(a + h) - f(a)] / (a + h - a)
4. Simplify further by canceling out common terms:
f^1(a) = lim(h->0) [f(a + h) - f(a)] / h
5. Finally, evaluate the limit as h approaches 0. The calculated value will be the derivative of the function at point a.
Remember that this definition gives you a general formula for finding the derivative at any point a for a given function. To solve specific problems, you will need to substitute the actual function and value for a into the equation.
Hope this explanation helps you understand how to use the definition to find the derivative!