#     arcsin 7

```Practice Gateway:
1)
f  x   6kx6 
2)
f  x 
k
 6e6 kx
6
x
3)
1
 2 x ln  x   32 x
x
f  x   arcsin  7t  97   arctan 16  3t 
4)
f  x   tan 4  7 x 
5) Given f  x  
6) Given f  x  
7) If f  x  
1
Use the limit definition of the derivative to find f   x 
x
3 x 2
1  x3

f
x

find


x3  1
 x3  1 1  x3 x3  1
x , find the equation of the tangent line to f at x = 4
8)
x
f  x
1.0
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
a) Estimate f  1.3
b) Estimate f  1.35 
9) Draw a graph of f(x) given the following information about f   x  and f   x 
f   x   0,  , 3 and  2,  
f   x   0,  3, 2 
f   x   0,  , 1
f   x   0,  1,  
LABEL local maximums and minimums and inflection points and their x coordinates.
10) The cost in dollars (in hundreds of dollars) to produce q quarts of ice cream is C  f  q  .
Interpret the following expressions in plain English.
a.
f  200   600
b.
f   200   2
c.
f   200   0 and f   200   0
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