2.2 Worksheet #1
Instantaneous Slope
Use the limit definition of slope to find the (instantaneous) slope of the given function at the given x value:
1. y = x2 at x = 3
2. y = 3x at x = 2
3. y = x3 at x = 2
4. y = x2 + 1 at x =0
5. y = 4 at x = 100
6. y = 2x2 – 3 at x = 5
7. y
1
x at x = 4. f ( x)
8. 4 x2
at x = 1
2.1 Worksheet #2
Definition of the Derivative
Given the equation, (a) Find the slope of the curve at the given point
(b) Find an equation of the tangent line
(c) Find an equation of the normal line
(d) Draw the graph of the curve, the tangent line and the normal line in the same square viewing
window. 1. y = x2 at x = – 2 2. y = x2 – 4x at x = 1
3. y
4. y
1
x 1 at x = 2
x 2 3x 1 at x = 0