Exercise set 3.5
- 1. EXERCISE SET 3.5 Graph the following functions. Find all critical points, extrema, inflection points, intervals of increasing and decreasing, and intervals of concave up and concave down. Show sign-charts for y, y’, and y’’. 4 2 4 3 1. y x 4x 2. y x 3x 5 3 3 5 3. y x 3x 4. y 5x x 4x 12 x 5. y 2 6. y 2 1 x x 2 2 2 2 7. y 3x 3 2x 8. y x 3x 3 3 3 2 9. y 5x 5 3x 10. y x 5x 5 Review HW 1. Given f(x) = 2x2, use the defintion of difference quotient to find f '(x). 1 x x 2 a. lim 2 as x 1 b. lim as x 2 x x 2x 2 2. Find the limits, if the answer is + or - , state so. 3. Find the derivative A. f(x) = - 4x3 + 2x2 B. f(x) = (3x +1)5 / (2x2 – 1)3 C. y = Tan( 3x 3 – 4 ) D. y = Sin ( Cos ( x 2 – 1 ) )
- 2. E. f(x) = Cos( 3x - 4 ) (4x3 - 2 / x3) F . y = LN2 (x + 1) 1 2 G. y ex 1 4. Find dy/dx using implicit differentiation y2 + x3y = x – 3 5. Given the implicit equation 2x2 + y 2 – 8x + 2 = 0, find the points where the graph has tangent lines with slope 1. 6. Find the second derivatives of the following functions. 2x 2x a. y b. y 2 x 5 x 1