Question

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

Answer 1

The Reqd. Slope`=e`.

Explanation:

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`.