1
151 WebCalc Fall 2002-copyright Joe Kahlig
In Class Questions
MATH 151-Fall 02
−
−
r (t), if →
r (t) =
1. Compute lim →
*
t→2
September 19
+
t2 − 4
, t3 + 1 .
t2 − 5t + 6
2. You are given the function f (x) and it is restricted to the interval [0, 4]. If f (0) = −0.5 and
f (4) = 4.5, can you conclude that there is some value c such that 0 < c < 4 and f (c) = 2?
Justify your answer.
3. Use the graph to answer the following questions.
6
5
4
3
2
1
−7
−6
−5
−4 −3
−2
−1
−1
1
2
3
4
5
6
7
8
−3
−4
(a) At what values of x is the function discontinuous?
(b) Find the average rate of change from x = −1 to x = 3.
(c) Compute the slope of the secant line going thru the points at x = −1 to x = 3.
(d) At what values of x does the function not have a derivative?
(e) Compute the slope of the tangent line at x = 7.
(f) What is the equation of the tangent line at x = −5?
(g) Compute f 0 (−1)
(h) For what values of x is the instantaneous rate of change equal to zero?
4. Set up the difference quotient for f (x) = x2 + 1 at x = 2. Now simplify the difference quotient.