Only do questions #1 a,c,e,h #3a, #4 Find the derivative for each of the following. a. y = cos(-7x) b. y = -/2sin(4 + 5x) C. f(x) = sin 3(x4) d. y = 4xsin*(5 - 9x)-1 e. f(x) = cos4(sin2x) y = Xcos g . f(x) = 1+ cos x h . 1 - sin2x y = cos-4x - sin3x i. For the following question, make sure to use exact values from the unit circle and do not simply plug your numbers into a calculator. 2. Find the equation of the tangent to the given curve for each of the following. a. y= - 3cosx at (, 1) b. f(x) = sin(sinx) at x = ~ 3. Find the critical numbers, the intervals of increase and decrease, and any maximum or minimum values. a. y = COS X, -It S X ST b . y = sinx - Cosx, -It S x S n 4. If f(x) = sin xcos5x, evaluate f"' (") Only do questions #1a,b,e, #2a, #5, #6. 1. Differentiate each of the following. a. f(x) = In(x2 + 1) b. y = exl C. f ( x ) = 2x+3 V4X -5 d. y = log10(1 - x + x3) e. f( x ) = ex f. y = V1 + In (x) 2. Find the equation of the tangent line to each curve at the given point. a. f(x) = 4*, (0, 1) b. iny (2.718, 2.718) 3. Use logarithmic differentiation to find the derivative for each of the following. a . y = x5e*Vx2 - x+1 y = Vxx 4. On what intervals is the function 2x3 - yzInx increasing or decreasing? 5. The initial size of a bacteria culture is 1 200. After 6 h, there are 8400 bacteria. Find the number of bacteria after t hours. Find the number of bacteria after 10 h. C. Find the rate of growth after 6 h. 2 When will the bacteria population reach 20 000? Discuss the curve y = In(9 - x2) under the following headings. a. Domain. b . Intercepts. C . Symmetry. d. Asymptotes e. Intervals of increase or decrease Maximum or minimum values Concavity Sketch of the curve