MATH 1610 Study Guide - Midterm Guide: Relative Growth Rate, The Tangent, Power Rule
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MATH 1610 Full Course Notes
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The derivative of a unction f at a number a, denoted by f"(a), is. Solution: a point p on the curve = + is such that the tangent line at p is parallel to the line = +. Solution: y = x2 + 2 4 y = 2x + 2. Since the tangent line is parallel to y = 4x + 11, then: 2x + 2 = 4, x = 1. The product rule () = (), g(4) = 2, g"(4) = 3,find f"(4). [() (x)] =()() +()() f"(x) = ( ) () + () =14 2 + 2 3 = 6. 5. The quotient rule f(x) = + , find f"(x). =( + 1) ( 1) ( + 1)2. Practice questions: f(x) is differentiable. f(1)=2,f(2)=3,f"(1)=4, f"(2)=5, f"(3)=6. If g(x) = f[ xf[ xf(x) ] ], find g"(1). Solution: g"(x)= () () g"(1)= 1 1(1) [ 1(1) + 1 1(1) 1 (1) + 1(1) ]
