Posted by sara on Monday, July 28, 2014 at 2:05pm.
dy/dx and d2y/dx2.
x = et, y = te−t
- math - Steve, Monday, July 28, 2014 at 3:09pm
x = e^t
y = te^-t
dy/dx = y'/x'
d^2/dx^2 = (x'y"-x"y')/x'^3
= ((e^t)(t-2)e^-t - (e^t)(1-t)e^-t)/e^3t
or, do it directly
x = e^t, so
y = lnx/x
y' = (1-lnx)/x^2 = (1-t)e^-2t
y" = (2lnx-3)/x^3 = (2t-3)e^-3t
- math - sara, Monday, July 28, 2014 at 4:55pm
thanks. so how woudl i find For which values of t is the curve concave upward?
- math - Steve, Monday, July 28, 2014 at 6:37pm
just as usual. Where is y" positive?
e^-3t is always positive, so all you need is
2t-3 > 0
t > 3/2
e^3/2 = 4.48, and you can see from the graph that it is concave upward for x > 4.48
Answer This Question
More Related Questions
- Second Derivatives - If y = 2 f(g(x)), then d2y/dx2 = ? The d2y/dx2 means the ...
- Calculus-Math - Find d2y/dx2 in terms of x and y. x^2y^2-2x=3
- calculus - Find d2y/dx2 in terms of x and y. y5 = x6
- caculus 1, please help - Find d2y/dx2 in terms of x and y. y5 = x6
- maths - x=tcost & y=t+sint then find dx2/d2y
- Maths - If y is a function of x and z = e^z, show that: x (dy/dx) = (dy/dz) and...
- math - d2y/dx2+9y=cos2x+sin2x
- Calc 2 - Find the second derivative (d2y/dx2) for the curve given by x = 2Ěcos...
- integral - Find dy/dx and d2y/dx2 if y= definite integral sign where a= 1 and b...
- Integral - Find dy/dx and d2y/dx2 if y= definite integral sign where a= 1 and b...