Final Exam Review
Math 1325.C02
Professor Merrill
1.
Find the value x = a where the function is discontinuous. For each point of discontinuity,
find lim f(x) , b) lim f(x) , c) lim f(x) , and d) f(a) if it exists
xa
xa
xa
2.
Find the a) average rate of change over the given interval, and b) instantaneous rate of
𝑥+4
change at the first x-value of 𝑦 = 𝑥−1 from x = 2 to x = 5.
3.
Find the equation of the line tangent to f(x) = 2√𝑥 − 1 at x = 5.
4.
Find the limit, if it exists, of lim
x2  16
x4 x  4
x2  6x  8
3
x  x  2x  1
5.
Find the limit, if it exists, of lim
6.
Find the limit, if it exists, of lim
7.
Find the derivative of y = -7x2e-3x
8.
Find the derivative of y = ln(5x + 3)
x 2
x 8
3
x 8
9.
A sum of $1500 is deposited in an account with an interest rate of r percent per year,
compounded daily. At the end of 5 years, the balance in the account is given by
1825
r


A  1500  1 

 36,500 
. Find the rate of change of A with respect to r for a 6% interest
rate.
10. Graph the function f(x)  
4 3
x  x2  30x  7 . Considering the domain, find the critical
3
points, regions where the function is increasing/decreasing, inflection points, regions where
the function is concave up/down, and intercepts (where possible).
11. A company wishes to manufacture a box with a volume of 36ft3 that is open on top and is
twice as long as it is wide. Find the dimensions of the box produced from the minimum
amount of material.
12. Given the revenue and cost functions R = 50x – 0.4x2 and C = 5x + 15, where x is the daily
production (and sales), find a) the rate of change of revenue with respect to time and b) the
rate of change of cost, with respect to time, when 40 units are produced daily and the rate
of change of production is 10 units per day.
13. Find dy/dx of x2 – 4y2 = 3x3y4
2
14. Find the cost function for the marginal cost of C'(x)  x 3  2 given that 8 units cost $58.
15. Graph the function f(x) = 2x – 14. Find the area between the x-axis and f(x) over the
interval [6, 10].
Review the concept checks at the end of chapters 3 - 7 (chapter review). There may be 3-4
multiple choice questions similar to these.