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Sec. 1.pdf - Instructor:ChristineMcDonald Course:...

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Student: osita ezulike Date: 9/25/16 Instructor: Christine McDonald Course: MAC2233­218926 BUSINESS CALCULUS I ­ INTERNET Assignment: Sec. 1.4 Find an equation for the tangent line to the graph of the given function at . ( − 1, − 1) f(x) = x 3 The slope, m, of the tangent line at is given by the limit below. (x,f(x)) m = lim h 0 f(x + h) − f(x) h Which limit below is equal to the slope, m, of the tangent line to the given function at the given point? A. lim h 0 ( − 1 + h) − ( − 1) h B. lim h 0 ( − 1 3 + h 3 ) − ( − 1) 3 h C. lim h 0 ( − 1 + h) − ( − 1) h D. lim h 0 ( − 1 + h) 3 − ( − 1) 3 h Substitute and simplify. Use the fact that . (x + h) 3 = x + 3hx + 3h x + h 3 2 2 3 m = lim h 0 f(x + h) − f(x) h = lim h 0 ( − 1 + h) 3 − ( − 1) 3 h = lim h 0 ( − 1) 3 + 3h( − 1) 2 + 3h 2 • − 1 + h 3 − ( − 1) 3 h Now simplify the numerator. m = lim h 0 ( − 1) 3 + 3h( − 1) 2 + 3h 2 • − 1 + h 3 − ( − 1) 3 h = lim
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