What is the slope of #f(x)=-e^x/x^2# at #x=1#?

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Answer 1 · 2016-09-24T09:09:11

The Reqd. Slope#=e#.

We know that slope of a curve # C : y=f(x)=-e^x/x^2=-x^-2e^x#

at #x=1" is nothing but "f'(1).#

#f(x)=-x^-2e^xrArr f'(x)=-{(x^-2)(e^x)'+(e^x)(x^-2)'}#

#=-{(x^-2)e^x+e^x(-2x^-3)}#

#=-e^x(x^-2-2x^-3)#

#rArr f'(1)=-e^1(1^-2-2*1^-3)#

#=-e(1-2)=e#.

Hence, the Reqd. Slope#=e#.