1. Graph and analyze the critical points, extrema, inflection points, intervals of increasing/decreasing, and intervals of concave up/down for 10 functions. 2. Review homework on finding derivatives using the definition of the difference quotient and evaluating limits. Find the derivatives of 6 functions. 3. Use implicit differentiation to find the derivative of one function defined implicitly and to find points with tangent lines of slope 1 for another implicit function. 4. Find the second derivatives of two functions.

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