Gradient help (1 Viewer)

[iampeterr]

The line y=mx is a tangent to the curve y = logx / x
find the value of m.

it is given that dy/dx = 1 - logx / x^2

&

Hence, find the values of k such that the equation kx = logx / x has exactly two solutions

thanks !

 

[Beaconite]

for first bit, differentitae y= In x / x and equate it with mx; find m

 

[Beaconite]

for second bit, integrate dy/dx= 1 - In x/x^2 with respect to x

 

[iampeterr]

integrate dy/dx= 1 - In x/x^2 with respect to x

wouldn't that just get me back to logx / x ? :S

 

[Sindivyn]

for second bit, integrate dy/dx= 1 - In x/x^2 with respect to x

Can't you just find m using what you said in your other post, then inspect the graph and state if m is less than or greater than that.

 

[Sanjeet]

The line y=mx is a tangent to the curve y = logx / x
find the value of m.

it is given that dy/dx = 1 - logx / x^2
thanks !

How do you find m? isn't there an infinite number of tangents to the curve and hence an infinite amount of tangents?