Posted by Hannah on Saturday, April 30, 2011 at 7:58pm.
e^x=0 and then (x+2)(x-2) so x=2, -2
2) differentiate: y=ln(6x^2 - 3x + 1)
1/(6x^2 - 3x + 1) * 12x-3
3) differentiate: y=e^-3x+2
-3 * e^-3x+2
4) evaluate: 2^4-x=8
2^4-x = 2^3
4-x = 3
-x=-1 so x=1
5) differentiate: x^3 + y^3 -6 =0
3x^2 + 3y^2
6) A rectangular garden has an area of 100 square meters for which the amount of fencing needed to surround the garden should be as small as possible.
a) draw a picture of a rectangle and select appropriate letters for the dimensions
I chose x and y
b)determine the objective and constraint equations
c) find the optimal values for the dimensions.
I am not sure for this one
Thank you for your help!!!
- Math(Please check. Thank You) - bobpursley, Saturday, April 30, 2011 at 8:28pm
1. e^x can never equal zero, but can approach it as x>>-infinity
But the roots are in fact -2,2
3 e^(-3x+2)=e^-3x * e^2
then y'= -3e^-3x * e^2=-3e^(-3x+2)
x^3+y^3=0 You can do implicit differentation, but I am not certain you know that.
y= cubroot x^3=x
6) xy=100 constraint
Perimeter= 2x+2y objective
dP/dx= 2+ d2(200/x)/dx= 2-400/x^2 =0
x=10 Y=10 is minimum fencing
- Math(Please check. Thank You) - Mgraph, Saturday, April 30, 2011 at 8:50pm
y'=-x^2/y^2, where y=(6-x^3)^(1/3)
- Math(Please check. Thank You) - bobpursley, Saturday, April 30, 2011 at 8:53pm
I agree, Mgraph, thanks.
- Math(Please check. Thank You) - Hannah, Saturday, April 30, 2011 at 11:22pm
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