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Analysis of Derivative and Line Equation for Quadratic Function in 2007

This document explores the relationship between a quadratic function and its derivative. The function is expressed as f(x) = x² - 7. By calculating its derivative, we find that f'(x) = 2x, which gives the slope at any point x. Specifically, at x = -3, the slope f'(-3) is evaluated to be -6. Using this slope and a point on the curve, the equation of the tangent line is derived in the form y = -6x - 16. The analysis highlights the importance of derivatives in understanding the behavior of functions.

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Analysis of Derivative and Line Equation for Quadratic Function in 2007

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  1. 2007 f(x) = x2-7 f’(x) = 2x So the ’lutning’ is given by 2x. So f’(x) = 2.-3 = -6. When x -3, y= x2 – 7  y = 2 x=-3; y= 2, k= -6 y=kx + m  y-kx=m  m=2-(-6.-3) = -16 Y= -6X- 16

  2. 2007

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