' Master the Equation of the Tangent in No Time! with IIT BHAU! 🚀

Welcome to another insightful lesson with IIT BHAU! 🫡

Today, we are diving deep into one of the most intriguing topics in calculus : The Equation of the Tangent

Understanding how to find the equation of a tangent is crucial for mastering the application of derivatives. A tangent line to a curve at a given point provides valuable information about the curve's behavior at that point. This concept is particularly important for students preparing for competitive exams like JEE and NEET.

In this lesson, we'll cover :

1. Definition of a Tangent : A line that touches a curve at one point without crossing it.

2. Calculating the Slope of the Tangent : Using the derivative \( f'(x) \) at the point of tangency.

3. Identifying the Point of Tangency : The coordinates \( (x_0, y_0) \) where the tangent meets the curve.

4. Formulating the Tangent Equation : Employing the point-slope form \( y - y_0 = f'(x_0)(x - x_0) \) to derive the equation.

5. Step-by-Step Process :
- Derive \( f'(x) \) of the function \( y = f(x) \).
- Substitute the x-coordinate into \( f'(x) \) to get the slope.
- Apply the point-slope form to find the equation of the tangent.

6. Examples and Practice Problems : We’ll work through several examples to ensure you understand every step of the process.

Whether you’re studying for exams or simply looking to enhance your understanding of calculus, this lesson is designed to provide clear, concise explanations and plenty of practice.

| Tangent, Derivative, Slope, Point of Tangency, Calculus, JEE Preparation, NEET Preparation, IIT BHAU |

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