theodore0307
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Can someone help me with this question.
View attachment 29911
View attachment 29911
Question on differentiation of exponential functions. (1 Viewer)
- Thread starter theodore0307
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I put the answer on my website. Please scroll all the way down the page. www.cambridgecoaching.com.au
Reza Bokat,
www.cambridgecoaching.com.au
Reza Bokat,
www.cambridgecoaching.com.au
y=xe^x
dy/dx= xe^x + e^x
= e^x(x+1)
= 0 for stationary points
As e^x never actually reaches 0, the only solution would be x= -1
Sub in that value for x into the equation y=xe^x, and you get the stationary point (-1, -1/e)
Then using second derivative or testing points you can show whether it's a relative maxima or minima.
As for sketching the curve, plot your stationary point, and you can determine the shape of the curve by subbing in very large/very small values of x to see the behaviour of x as it approaches infinity, e.g. sub in x=1000 and y=xe^x will approach a very large number.
dy/dx= xe^x + e^x
= e^x(x+1)
= 0 for stationary points
As e^x never actually reaches 0, the only solution would be x= -1
Sub in that value for x into the equation y=xe^x, and you get the stationary point (-1, -1/e)
Then using second derivative or testing points you can show whether it's a relative maxima or minima.
As for sketching the curve, plot your stationary point, and you can determine the shape of the curve by subbing in very large/very small values of x to see the behaviour of x as it approaches infinity, e.g. sub in x=1000 and y=xe^x will approach a very large number.
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