Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
- the tangent line to the graph of y=lnx\x is perpendicular to the line x=7 at the point where?
The line x = 7 is perpendicular to x axis. Hence, it's slope is infinity.
The tangent line that is perpendicular to this line will be parallel to x axis.
And it's slope will therefore be 0
Hence, we need to find the point on the curve y = lnx/x where the slope is 0, i.e. where dy/dx = 0
Without wasting your time, differentiate both sides w.r.t x to get:
dy/dx = (x.1/x - lnx)/x2 = (1 - lnx)/x2
Clearly dy/dx will be 0 when
1 - lnx = 0
Or, lnx = 1
Or x = e1 = e
and y = ln(e)/e = 1/e
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