Estimate the slope of the tangent line to the curve f(x) = x2 at the point (1, f(1)) by examining the trend in the secant slopes calculated.

f'(1) = 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

The definition of a derivative is the slope of the tangent line.

Derivative Notation

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

f(x) = x²

Point (1, f(1))

Step 2: Differentiate

Step 3: Find Slope

Use the point (1, f(1)) to find the instantaneous slope

This tells us that at point (1, f(1)), the slope of the tangent line is 2. We can write an equation using point slope form as well: y - f(1) = 2(x - 1)

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step-by-step explanation: