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2.2 Basic Differentiation Rules Objectives: Find the derivative using the Constant Rule, the Power Rule, the Constant Multiple Rule, the Sum and Difference Rules; find derivative of the sine and closing functions; use derivatives to find rates of change. 2.2 #2 Assignment: On your own paper. Find the slope of the graph at the given point. 1. f ( x ) = -2 ; (1, 3 ) 3 2. f ( x ) = 3- 3 5 x 5' 3. y = 3x3 -6; (2, 18) 4. y = (2x +1); (0, 1) 5. f (0) = 4sino - 0; (0, 0) 6. g (t) = 2+3cost; (1, -1) Find the derivative of the function. 7. f ( x) =x2 +5-3x-2 8. f ( x) = x2 - 3x - 3x-2 9. g (t ) = +2 - 10. f ( x ) = X' - 3x2 + 4 x 2 11. y = x(x2 +1) 12. f ( x ) = Vx-68/x 13. f (x) = x213 - x 1/3 + 4 14. f ( x) = 6Vx +5cosx 15 . f ( x ) =_ 2 + 3 cos x 3X Find an equation of the tangent line to the graph of f at the given point. 16. y = x4 - 3x2 +2; (1, 0) 17. y = x' + x; (-1, - 2) 18. f ( x) 2 4 X3: (7, 2 ) Determine the points (if any) at which the graph of the function has a horizontal tangent line. 19. y = x4 - 8x2 +2 20. y = X' + x 21. y = 1 * 2 22. y = x2 +1 23. y = x + sinx, 05x