### Problem StatementIf \( f(x) = 2x^2 - 9x + 4 \), find the equation of the line tangent at \( x = 2 \).### Explanation:To solve this problem, follow these steps:1. **Find the derivative** of the function to determine the slope of the tangent line at any point \( x \). Given \( f(x) = 2x^2 - 9x + 4 \), The derivative, \( f'(x) \), is calculated as follows: \[ f'(x) = \frac{d}{dx}(2x^2 - 9x + 4) = 4x - 9 \]2. **Calculate the slope at \( x = 2 \)** by substituting \( x = 2 \) into the derivative: \[ f'(2) = 4(2) - 9 = 8 - 9 = -1 \]3. **Find the point on the curve** at \( x = 2 \) by substituting \( x = 2 \) into the original function: \[ f(2) = 2(2)^2 - 9(2) + 4 = 8 - 18 + 4 = -6 \]4. **Use the point-slope form** to write the equation of the tangent line: The point-slope form of a line is given by: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1) = (2, -6)\) and the slope \( m = -1 \). Substitute these values: \[ y - (-6) = -1(x - 2) \] \[ y + 6 = -x + 2 \] \[ y = -x + 2 - 6 \] \[ y = -x - 4 \]Hence, the equation of the tangent line at \( x = 2 \) is \( y = -x - 4 \).

Name: ### Problem StatementIf \( f(x) = 2x^2 - 9x + 4 \), find the equation
Uploaded: 2024-03-20T06:46:42.000Z
Channel: Bartleby
Description: ### Problem StatementIf \( f(x) = 2x^2 - 9x + 4 \), find the equation of the line tangent at \( x = 2 \).### Explanation:To solve this problem, follow these steps:1. **Find the derivative** of the function to determine the slope of the tangent line