The equation of the tangent line to the curve y = x^2 at the point (2, 4) is:

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What’s inside this PDF?

Question: The equation of the tangent line to the curve y = x^2 at the point (2, 4) is:

Options:

y = 2x
y = 4x - 4
y = 4x - 8
y = x + 2

Correct Answer: y = 4x - 8

Solution:

The slope of the tangent at x = 2 is f\'(x) = 2x, so f\'(2) = 4. The equation of the tangent line is y - 4 = 4(x - 2), which simplifies to y = 4x - 8.

The equation of the tangent line to the curve y = x^2 at the point (2, 4) is:

Practice Questions

The equation of the tangent line to the curve y = x^2 at the point (2, 4) is:

y = 2x
y = 4x - 4
y = 4x - 8
y = x + 2

Questions & Step-by-Step Solutions

The equation of the tangent line to the curve y = x^2 at the point (2, 4) is:

Step 1: Identify the function. The function is y = x^2.
Step 2: Find the derivative of the function to get the slope of the tangent line. The derivative f'(x) = 2x.
Step 3: Calculate the slope at the point x = 2. Substitute 2 into the derivative: f'(2) = 2 * 2 = 4.
Step 4: Use the point-slope form of the equation of a line. The point is (2, 4) and the slope is 4.
Step 5: Write the equation using the point-slope form: y - y1 = m(x - x1), where (x1, y1) is (2, 4) and m is 4.
Step 6: Substitute the values into the equation: y - 4 = 4(x - 2).
Step 7: Simplify the equation. Distribute 4: y - 4 = 4x - 8.
Step 8: Add 4 to both sides to isolate y: y = 4x - 8.

Differentiation – Understanding how to find the derivative of a function to determine the slope of the tangent line.
Point-Slope Form of a Line – Using the point-slope form to write the equation of a line given a point and a slope.
Quadratic Functions – Recognizing the properties of quadratic functions and their graphs.

The equation of the tangent line to the curve y = x^2 at the point (2, 4) is:

What’s inside this PDF?

The equation of the tangent line to the curve y = x^2 at the point (2, 4) is:

Practice Questions

Questions & Step-by-Step Solutions

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