Thursday

April 24, 2014

April 24, 2014

Posted by **tom** on Thursday, April 4, 2013 at 11:18am.

- math -
**Reiny**, Thursday, April 4, 2013 at 12:26pmconsider the two separate functions

y = e^(2x) and y = k√x

To have 1 real root, they must touch each other

that is, they must have a common tangent at their point of contact

so for the first : dy/dx = 2e^(2x)

for the second: dy/dx = (1/2)(k)x^(-1/2)

they must be equal

4e^(2x) = k/√x ---> k = 4e^(2x) √x

from the original: k = e^(2x)/√x

so 4e^(2x) √x = e^(2x)/√x

4√x = 1/√x

cross-multiply

x = 4

then using one of the expressions for k

k = e(2x)/√x = e^8/2

check my arithmetic

**Related Questions**

calc - analyze the function ln x = cx^2 to find the unique value of c such that ...

Calculus AB - Analyze the function ln x=cx^2 to find the unique value of c such...

math - If y varies diretly with x, write an equation for the direct variation. ...

math - A study was conducted to investigate the relationship between the resale ...

math - A study was conducted to investigate the relationship between the resale ...

maths - find value of p such that the equation (x+1)(x+2)=p

Math - 1)let k and w be two consecutive integers such that k<x<w. If log ...

math - can someone correct this for me... solve: -4(2x - 3) = -8x + 5 my answer...

Find the value of K (Polynomial) - Dtermine the value of K such that -2 is cone ...

SAT math - I've really been stuck on these questions: 1. If ( x + 2 y )= -4 and ...