Expert: Paul Klarreich - 3/16/2009

Question
Hello, I was wondering if you can please help me find the solutions to these 5 problems i have left..please!! i will appreciate so much!
Thankyou!


1)Construct a linear approximation for the function at x=-1   y=x^4-3x^3=2x^2-x+7

a) -18 x + 6
b) -18 x - 4
c) -14 x + 6
d) - 14 x - 4

2)Let P(x) (in thousands of dollars) be the profit from producing and selling x number of widgets. If P'(1000) = 236.74, what is the profit (approximately) obtained from selling the 1001st widget?

a) $236,740,000
b) $236,740
c) $236.74
d) Without knowing P(x) this can not be determined

3)Use a graphing calculator to find the slope of the tangent line to the function at x = -1.
y=x^4-3x^3+2x^2-x+7

a) - 4
b) - 14
c) - 18
d) - 22

4)Construct a linear approximation for the function at x = 2. f(x)=xe^x

(a) y = 22.17x - 29.56
(b) y = 14.78x - 14.78
(c) y = 22.17x + 14.78
(d) y = 14.78x - 29.56

5)Find the differential dy given:
f(x)=lnx+2

a.ln xdx
b.1/x(dx)
c.(lnx+2)dx
d.(1/x+2)dx

Answer
Questioner:   Sarah
Category:  Calculus
Private:  Yes
 
Subject:  Help!
Question:  Hello, I was wondering if you can please help me find the solutions to these 5 problems i have left..please!! i will appreciate so much!
Thankyou!


1)Construct a linear approximation for the function at x=-1   y=x^4-3x^3=2x^2-x+7

a) -18 x + 6
b) -18 x - 4
c) -14 x + 6
d) - 14 x - 4

1) Find dy/dx at x = -1.  This is your m.
Find f(-1).  This is your y.  
Now use  x = -1, and the m and y to write the equation of a line.
...................................

2)Let P(x) (in thousands of dollars) be the profit from producing and selling x number of widgets. If P'(1000) = 236.74, what is the profit (approximately) obtained from selling the 1001st widget?

a) $236,740,000
b) $236,740
c) $236.74
d) Without knowing P(x) this can not be determined


             P(1001) - P(1000)
P'(1000) ~~  ------------------
               1001 - 1000   

That should do it for you.

=========================================

3)Use a graphing calculator to find the slope of the tangent line to the function at x = -1.
y=x^4-3x^3+2x^2-x+7

a) - 4
b) - 14
c) - 18
d) - 22

Sorry, I never learned to use one. [I am very 20th-century and we didn't have them.]
..........................................
4)Construct a linear approximation for the function at x = 2. f(x)=xe^x

(a) y = 22.17x - 29.56
(b) y = 14.78x - 14.78
(c) y = 22.17x + 14.78
(d) y = 14.78x - 29.56

See #1.

....................

5)Find the differential dy given:
f(x)=lnx+2

a.ln xdx
b.1/x(dx)
c.(lnx+2)dx
d.(1/x+2)dx

dy = f'(x) dx.

Differentiate, etc.


Note: Don't mark PRIVATE.  I change it, anyway.  If you don't want anyone to see your question or answer, you have to send it elsewhere.