Basic SKiLLs PrRACTICE For Exercises 1 - 3, use the Generalized Power Rule to find the derivative of the function. 1. f(x)=(4x+12) 2. g =(126+33x)" 1,5 ,1 1 and 12 3. f(=(8t+e') d 5 For Exercises 4 - 7, use the Generalized Exponential Rule to find d_' for the function. X 4. y=e 5. '='\\E_Ii_3 6. v= 89_1512x_5 7. y= 10714 For Exercises 8 - 11, use the Generalized Logarithm Rule to find f " (x). 8. f(x)=In(4+x) 9. f()=1n(9-13x2+17) 10. f(x)=log, (H +55.x3) X 11. f(x)=logs (36x"" = 12x" +x - 1) For Exercises 12 - 14, find the slope of the line tangent to the graph of f at the given x-value. 12. f(0 = (77 +55) atx=-2 13. flx)= 6 22 g x =0 14. f(x) =log, (4,13 + 16.1') atx=1 For Exercises 15 - 17, find the equation of the line tangent to the graph of the function at the given x-value. 7 15. f(x)=("-2) atx=1 16. g(x) = (,.t"'+h.r2+!2x atx=0 17. h(x) = ln(x3+3x+3] atx=-1 1 - 4 18. Given f(x)= g(.r' 3x"+3x) , find the equation of the line tangent to the graph of f at x = 2. Use technology to graph f and the tangent line on the same axes. For Exercises 19 - 21, find the x-value(s) where the graph of f has a horizontal tangent line. 19. f(0=(2-4)" v 17,19,23 and 27 21. f(x)=In(x*+11x+31) For Exercises 22 - 25, use the Alternate Form of the Chain Rule to find :L 22. y= Vuand u=8x"-8 23. y= 8' 8and u = Vx 24. y=In(z)-13zand z= 2" -3 + 1 [ 25. y=andt=e"+7Tx T+ 26. The price-demand function for a brand of diploma frame is given by p(x) = (=0.01x-2)* + 303, where p(x) is the price, in dollars, per frame when x frames are demanded. At what rate is the price changing when 400 frames are demanded? 27. The cost of making x high end toaster ovens is given by C(x) = x> + V13x+ 160 dollars. At what rate is the cost changing when 300 toaster ovens are made. In other words, what is the marginal cost when x = 3007 28. The function s(1) = 7 represents the position of a particle, in inches, after seconds. What is the Ly instantaneous velocity of the particle after 1 second? \f