Twhat point does the curve have maximum curvature? y = 7ex (x, y) = what happens to the curvature as x → ∞? κ(x) approaches as x → ∞.

Formula for curvature for a well behaved curve y=f(x) is

K(x)=

The given curve is y=7

k(x)=

For Maxima or Minima

→

  [not possible ∵there exists no value of x satisfying these equation]

→

Solving this we get

x=

As you will evaluate <0 at x=

So this is the point of Maxima. we get y=7×1/√98=1/√2

(x,y)=[,1/√2]

k(x)=

k(x)=

k(x)=0

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