quiz2_solution

Then we will plug in x 2 to this formula to get the

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Unformatted text preview: for f (x) = x − 2x − 3. Then, we will plug in x = 2 to this formula to get the slope of the tangent line at the point (2, −3). f ( x + h ) − f ( x) ((x + h)2 − 2(x + h) − 3) − (x2 − 2x − 3) = lim , h→ 0 h→ 0 h h (x2 + 2xh + h2 − 2x − 2h − 3) − (x2 − 2x − 3) = lim , h→ 0 h x2 + 2xh + h2 − 2x − 2h − 3 − x2 + 2x + 3 = lim , h→ 0 h 2xh + h2 − 2h = lim , h→ 0 h = lim (2x + h − 2), lim h→ 0 = 2x − 2 . Therefore, the slop of the tangent line at the point (2, −3) is 2 × 2 − 2 = 2. Next, since this tangent line has sl...
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