Math 2413
EMCF 08
EMCF 08
1. Let f(x) be a polynomial function such that f(−4) = −2,f ′ (−4) = 0 and f ′′ (−4) = −1. Classify the point
(−4,−2).
a) inflection point
b) local maximum
c) local minimum
d) intercept
e) none of the
2. Let f(x) be a polynomial function such that f(2) = −4,f ′ (2) = 0 and f ′′ (2) = 5. Classify the point (2,−4).
a) local minimum
b) intercept
c) local maximum
d) inflection point
e) none of the these
3. Suppose f(x) is an invertible differentiable function and f(2) = −4, f(−4) = 5,f ′ (2) = −5,f ′ (5) = 1.

Find f 1  4 .
 
a) 5
b) −1/5
c) −5
d) 1/5
e) 1
4. Suppose f(x) is an invertible differentiable function and f(−5) = −3,f(−3) = −1,f ′ (−5) = −4,f ′ (−1) = −2 .

Find f 1  3 .
 
a) 4
b) −4
c) 1/4
d) −1/4
e) −1/2
Math 2413
EMCF 08
5. Suppose f(x) is an invertible differentiable function and the graph of f passes through the points

(6,−2) and (−2,7). The slope of the tangent line to the graph of f at x = −2 is 3/4 . Find f 1 7  .
 
a) 3/4
b) 1/2
c) 4/3
d) −4/3
e) 1/6
6. Suppose f(x) is an invertible differentiable function and the graph of f passes through the points

(3,6) and (6,2) . The slope of the tangent line to the graph of f at x = 6 is 3/2 . Find f 1 2  .
 
a) −2/3
b) 2/3
c) 3/2
d) −1/6
e) 1/3
7. Find the slope of the tangent line to the graph of f x  e2 x 4 x at the point where x = 0.
2
a) 1/4
b) −1/4
c) 4
d) −4
e) 0
8. Find the slope of the tangent line to f x   2esin( 3 x ) at the point where x = 0.
a) −1/6
b) 6
c) 0
d) −6
e) 1/6
Math 2413
EMCF 08
 x4 y3 
 using properties of logarithms.
9. Expand: ln 
7 
 2w 
a) 4ln(x)−3ln(y)−7ln(w)
b) 3ln(2)+4ln(x)−3ln(y)−7ln(w)
c) −ln(2)+4ln(x)+3ln(y)−7ln(w)
d) −ln(2)+4ln(x)+3ln(y)+7ln(w)
e) −ln(2)−4ln(x)+3ln(y)+7ln(w)
 2 x3 y 6 
 using properties of logarithms.
10. Expand: ln 
5 
 5w 
a) ln(2)+3ln(x)+ln(5)−6ln(y)−5ln(w)
b) ln(2)+3ln(x)−ln(5)+6ln(y)−5ln(w)
c) ln(2)+3ln(x)−ln(5)+6ln(y)+5ln(w)
d) 3ln(x)−6ln(y)−5ln(w)
e) ln(2)−3ln(x)−ln(5)+6ln(y)+5ln(w)
11. The graph of (the derivative of ) is shown below. At what value of does the graph of
change from increasing to decreasing?
a) 0
b) 1/2
c) – 1
d) 2
Math 2413
EMCF 08
12. The graph of f ’(the derivative of f ) is shown below. At what value of does the graph of change from
decreasing to increasing?
a) -2
b) 0
c) 4
d) 2