University of Illinois at Chicago

### Question Description

I’m studying for my Calculus class and need an explanation.

I need the questions in the attached file solved thoroughly and neatly.

Name___________________________________ A = Pert Math 145-201 A = P(1 + r/n)nt Exam #2

Find the derivative for problems 1-8. 1)y = 3x5 - 7x2 - 4 x2 . 1)

2)y = 3t-4 - 5t-1 2)

3)f(x) = (x2 + 2)3 3)

4)f(x) = (ln x)4 4)

5)y = t7(t3 + 8)5 5)

1

6)f(x) = ln (x9) 6)

7)f(x) = 9ex - 6x + 2 7)

8)f(x) = 1 + ln ( 5 x4) 8)

Find all values of x for the given function where the tangent line is horizontal. 9)f(x) = x (x2 + 1)3 9)

10)f(x) = 3x3 - 2x2 - 9 10)

2

Solve the problem. 11)A publishing company has published a new magazine for young adults. The monthly sales S (in thousands) is given by S(t) = 800t t + 2, where t is the number of months since the first issue was published. Find S(3) and S'(3) and interpret the results.

11)

Find the equation of the line tangent to the graph of f at the indicated value of x. 12)f(x) = 1 + 3ex; x = 1 12)

13)f(x) = 5 ln x; x = 1 13)

Provide an appropriate response. 14)Find t to four decimal places. e -0.07t = 0.05

14)

3

Solve the problem. 15)What will the value of an account (to the nearest cent) be after 8 years if $100 is invested at 6.0% interest compounded continuously?

15)

16)For the problem above, find the value of the account if the interest was compunded quarterly instead of continuously.

16)

17)How long will it take for $8400 to grow to $14,600 at an interest rate of 9.4% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

17)

18)How long will it take money to double if it is invested at 5.25%, compounded continuously? Round your answer to the nearest tenth.

18)

Extra Credit: find the second derivative. 19)y = 8 + 5 x 4

19)

Extra Credit: find the first derivative. 20)y = ln(ln 7x) 20)

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