We have an answer to "What is the slope of f(x)=−exx2 at x=1?"

Ethan Mcfarland

Answered question

2022-03-12

What is the slope of

f (x) = - \frac{e^{x}}{x^{2}}

at x=1?

Kiera Tran

Beginner2022-03-13Added 5 answers

We know that slope of a curve

C : y = f (x) - \frac{e^{x}}{x^{2}} = - x^{- 2} e^{x}

at x=1 is nothing but f'(1)

f (x) = - x^{- 2} e^{x} \Rightarrow f^{'} (x) = - \leq f t {(x^{- 2}) {(e^{x})}^{'} + (e^{x}) {(x^{- 2})}^{'} r i g h t}

= - \leq f t {(x^{- 2}) e^{x} + e^{x} (- 2 x^{- 3}) r i g h t}

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

\Rightarrow f^{'} (1) = - e^{1} (1^{- 2} - 2 \cdot 1^{- 3})

=-e(1-2)=e.
Hence, the Reqd. Slope = e.

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