Posted by **Eva** on Wednesday, April 6, 2011 at 10:43pm.

Let f(x)=e^(2x)-kx, for k greater than 0.

Using a calculator or computer, sketch the graph of f for k=1/9, 1/6,1/3,1/2,1,2,4. Describe what happens as k changes.

f(x) has a local minimum. Find the location of the minimum.

x= ____

Find the y-coordinate of the minimum.

y= _____

Find the value of k for which this y-coordinate is largest.

k= ______

How do you know that this value of k maximizes the y-coordinate? Find d^2y/dk^2 to use the second-derivative test.

d^2y/d^2k=

(Note that the derivative you get is negative for all positive values of k, and confirm that you agree that this means that your value of k maximizes the y-coordinate of the minimum.)

MY ANSWERS ARE=

Loc. min= 1

y-coordinate=1

k where y is largest= 2

d^2y/d^2k = 4e^(2x)

The only one I got right plugging in these values was k when y is largest...

## Answer this Question

## Related Questions

- Calculus (pleas help!!!) - Let f(x)=e^(2x)-kx, for k greater than 0. Using a ...
- how to sketch a graph of.. - Local minimum and local maximum imply that the ...
- Calculus I - Sketch the graph of f by hand and use your sketch to find the ...
- calculus - How to sketch the graph of a differntiable function y = f(x) that has...
- one more graph question - Hopefull the last one. :) Sketch the graph of a ...
- Calculus Please Help - A) If x^2+y^3−xy^2=5, find dy/dx in terms of x and...
- Calculus - For any constant c, define the function f_c(x)= x^3+2x^2+cx. (a) ...
- Calculus - For any constant c, define the function f_c(x)= x^3+2x^2+cx. (a) ...
- Math-Graphs - graph g(x)=4(x^3)-24x+9 on a calulator and estimate the local ...
- Calculus check - A function f(x) is continuous for all x and has a local ...