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