The equation of the tangent to the curve y = x^2 at the point (2, 4) is:
Practice Questions
Q1
The equation of the tangent to the curve y = x^2 at the point (2, 4) is:
y = 2x - 4
y = 2x
y = x + 2
y = x^2 - 2
Questions & Step-by-Step Solutions
The equation of the tangent 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. The derivative f'(x) = 2x.
Step 3: Calculate the slope of the tangent line at the point (2, 4). Substitute x = 2 into the derivative: f'(2) = 2 * 2 = 4.
Step 4: Use the point-slope form of the equation of a line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the point (2, 4) and m is the slope (4).
Step 5: Substitute the values into the point-slope form: y - 4 = 4(x - 2).
Step 6: Simplify the equation. Distribute the 4: y - 4 = 4x - 8. Then add 4 to both sides: y = 4x - 4.
Step 7: The final equation of the tangent line is y = 4x - 4.
