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Mods:
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Review for Calculus Quiz 2-1 and 2-2
1. Find the average rate of change over the given interval. Then give the equation for that
secant line. **Graph to check your answer.
a. y = x2 – x + 1 over [0, 3]
b. y = 
1
over [1, 3]
x
2. When you find a derivative at a number, what are you actually calculating? What are all the
terms that mean the same thing?
3. Use the definition of a derivative to find the derivative of y = 2x2 – 2 at x = 1.
*Point-slope form: y  y1  m( x  x1 )
4. Your answer for #3 should be f '(1)  4 . Now find the tangent line to y = 2x2 – 2 at x = 1.
5. What is the normal line to y = 2x2 – 2 at x = 1?
6. Use the definition of a derivative to find the instantaneous rate of change of
1
y= 
at x = 0.
x 3
7. Use the definition of a derivative to find f ’(x) if f(x) =
2
.
x6
8. Use the definition of a derivative to find
dy
of y = 5x2 – 2.
dx
9. Using #8, find the tangent line to y = 5x2 – 2 at x = 0.
10. What is necessary for a function to be differentiable at a point? (Definition of
differentiable)
11. What are the 4 features occur on a graph that make the function NOT differentiable at a
point? Why does each feature make it not differentiable? (Definition of differentiable)