\fDetermines the equation of a line tangent to a function Determines the key characteristics (intervals of increase/decrease, maximum/minimum points Answers questions, given a displacement function Solves problems related to optimization With a high degree of effectiveness NOW USING ALL OF THIS AND ONLY THIS NO OUTSIDE FORMULAS 1. Find the derivative. a. y = sin x b. y = sin x C. y = cos(4x + 9) d. y = cos (x + 3) e. y = x sin(x + 5) f. y = 50* g. y =0 h. y = xe 3x+1 i. y = In(x + 3) j. y = 5In (x + 4) k. y = 5 1. y = (x' + 2) (x] + 2x + 1)3 m. y = In(sin x) n. y = (x + Inx) 2. Find the equation of the tangent line to the functiony = in (x - 2) when x = 3. 3. Find the equation of the tangent line to the curve y = cos x when : = . Your solution should use radian measure. 1. Find the intervals of increasing'decreasing for the function /(x) =ale* 5. Find the minimum value(s) of the function f(x) = e - 2x. 6. The position of a particle as it moves horizontally is described by the given equation 8 - sint - cost, 0 s + $ 2n. If s is the displacement in metres and f is the time in seconds, find the maximum and minimum displacements.***ONL'I' USE THE INFORMATION GIVEN TO ANSWER THE QUESTIONS ANY OUTSIDE FORMULAS, Oi SOLVING THE ANSWER WILL BE REJEOTED MUST BE DONE ON PAPER WITH WORK SHOWN!!!!*"* REMEMBER YOUR Law of natural growth and decay. MUST BE ON PAPER AND DO NOT F"UT AN EIP'LA WORK REMEMBER THE Maximums and minimums of quadratic functions. The vertex of a parabola was either minimum point depending on whether it opened upwards or downwards. REMEMBER THE Derivative of natural logarithmic functions REMEMBER THE Laws of logarithms REMEMBER THE Equation of the tangent[y=m[1r.-x1}+v1 For questions it? - 10, sohre the problem by following the procedure for solving an optimization problem steps. Include a concluding statement that summarizes your answer and includes the correct units. PRODEDURE THAT MUSE BE FOLLOWED Step 1: Establish the variables and the equation Step 2: Find the derivative Step 3: Set the derivative equal to CI and nd the critical numberts] Step :1: Find the second derivative and confirm it is a maximum or minimum. Step 5: Conclusion Unrelated: Let a represent the Iiviclth oi the play.r area in m 1 at 3; represent the length of the play area in m Let P represent the perimeter In m. Let A represent the area In m2. Equation A = my Curve Sketching Procedure 1. Domain 2. |"tercepts 3. Sym metry 4. Aay'r'ptotes 5. l"tervals of i"crease or decrease E. Muimam and minimum points ?. I"terval.s of concav'ty 8. Points of i"f ection 9. Sketch the cu "ve MUST BE!!! MUST BE ON PAPER AND DO NOT PUT AN EXPLANATION WITH WORK Determines t"e derivative of a fwction. si'rple ancl comb'ned