Mathematics
UIC Calculus Derivative Tangent Lines of Graphs & Problem Solving Exercises

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)

### Unformatted Attachment Preview

Name___________________________________ A = Pert Math 145-201 Exam #2 A = P(1 + r/n) nt Find the derivative for problems 1-8. 3x5 - 7x2 - 4 1) y = . 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. x 9) f(x) = 2 (x + 1)3 10) f(x) = 3x3 - 2x2 - 9 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 , where t is the number of months since the t+2 11) first issue was published. Find S(3) and S'(3) and interpret the results. 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 13) f(x) = 5 ln x; x = 1 12) 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. 5 4 19) y = 8 + x 19) Extra Credit: find the first derivative. 20) y = ln(ln 7x) 20) 4 ...
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