https://file.aiquickdraw.com/mathbot/file/1728981981411rtq1a40i.jpg

To find the equation of the tangent to the curve \( f(x) = x^2 - 9 \) at \( x = 3 \), we will follow these steps:

1. **Find the derivative \( f'(x) \):**
   The derivative of \( f(x) \) gives us the slope of the tangent at any point on the curve.
   \[
   f(x) = x^2 - 9 \implies f'(x) = 2x
   \]

2. **Evaluate \( f'(3) \) to find the slope at \( x = 3 \):**
   \[
   f'(3) = 2(3) = 6
   \]
   So, the slope of the tangent at \( x = 3 \) is 6.

3. **Find the point on the curve at \( x = 3 \):**
   We need the coordinates of the point where the tangent touches the curve.
   \[
   f(3) = 3^2 - 9 = 9 - 9 = 0
   \]
   Therefore, the point of tangency is \( (3, 0) \).

4. **Write the

Given that f'(c) = lim_{x -> c} [(f(x) - f(c)) / (x - c)], find the equation of the tangent to the curve f(x) = x^2 - 9 at x = 3.

Learn how to find the equation of the tangent to the curve f(x) = x^2 - 9 at the point x = 3. This step-by-step guide covers key calculus concepts such as derivatives and tangent lines. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation