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SECTION 3.3 - DIFFERENTIATION RULES 2. Find the following: B) (x200 + 17x181 - 11x74 - 8) A) dx ( 5) [(x3+2x2+x) C) - [(x2 + x) (x - 4)] D) dx E) [(x2 + 2x + 3) (x3 - x2)] dx x2- 1) 3. Let f and g be differentiable functions defined by the table to answer the following: x 1 2 3 4 f (x) 3 4 f' (x) 4 W N - - W N g(x) 4 2 2 1 3 4 A) If h (x) = xf (x), find h' (2). B) If h(x) = f(x)g(x), find h'(1). C) If h(x) = _, find h' (4). g ( x )' D) If h(x) = x2 f ( x0 ) g ( x ) -, find h' (3). 76 | PageSECTION 3.3 - DIFFERENTIATION RULES 4. A car driving along a freeway with traffic traveled s(t) = t3 - 6t2 + 9t meters in t sec. A) Determine the time (in seconds) when the velocity of the car is 0. B) Determine the acceleration of the car when the velocity is 0. 5. Answer these more challenging problems (carefully). A) If f (x) = 5x4 - 3x3 + x2 -7, find f(4) (x). B) Find a 2nd degree polynomial, P(x), such that P(0) = 5, P'(2) = 8, and P"(1) = 6. C) Find all the points (a, f (a)) on the graph of the function f(x) = x3 + 2x - 15 in which the line tangent to f is parallel to y = 29x + 17. 77 | Page