Question

Given f(x) = 4 - 3x² find the limit definition using the derivative

Answer 1

The limit definition of the derivative for the function f(x) = 4 - 3x² is calculated by using the formula f'(x) = lim(h → 0) [(f(x + h) - f(x)) / h], resulting in the derivative -6x.

Step-by-step explanation:

The question regards finding the limit definition of the derivative of a function, specifically for the given function f(x) = 4 - 3x². To find the derivative using the limit definition, we use the following formula:

f'(x) = lim(h → 0) [(f(x + h) - f(x)) / h].

Applying this to f(x), we get:

1. Substitute the function into the formula: f'(x) = lim(h → 0) [(4 - 3(x+h)² - (4 - 3x²)) / h].
2. Simplify the expression inside the limit.
3. Cancel out terms and simplify further to find the derivative of the function.
4. After simplification, the result will be the derivative f'(x) = -6x.

This limit process is how we find the derivative of a function. In this case, it tells us the slope of the tangent line to the curve at any point x for the given function.