Question

Pretty please help me !! What is the slope of this graph when it is changing most rapidly ?

$A\left(x\right)=\frac{43}{1+64.4e^{\left(-0.79x\right)}}$

Answer 1

\[A\left(x\right)=\frac{43}{1+64.4e^{\left(-0.79x\right)}}\]

Answer 2

A(x)=\[\frac{43}{1+64.4e^{\left(-0.79x\right)}}\]

Answer 3

Yes

Answer 4

i am not sure what "slope of the graph when it is changing the most" means

Answer 5

most rapidly

Answer 6

maybe take the second derivative to find when the first derivative is largest

Answer 7

here is a picture, lets see if we can find the second derivative
http://www.wolframalpha.com/input/?i= \frac{43}{1%2B64.4e^{\left%28-0.79x\right%29}}+domain+-2..10

Answer 8

wow this is going to suck to do by hand
here is the derivative, and below is the second derivative
http://www.wolframalpha.com/input/?i=%282187.67+e^%280.79+x%29%29%2F%2864.4%2Be^%280.79+x%29%29^2&lk=1&a=ClashPrefs_*Math-

Answer 9

looks like the derivative has a local max at \(5.2723\) so that is the \(x\) value where the function is changing most rapidly

Answer 10

http://www.wolframalpha.com/input/?i=maximum++%282187.67+e^%280.79+x%29%29%2F%2864.4%2Be^%280.79+x%29%29^2

Answer 11

Okay thank you !!

Answer 12

yw, hope it is right