Question

Find the slope of the curve y=2/x at x=a.​

Answer 1

• We are given:- y=2/x
• We need to find the slope of the curve at x=a.

Explanation:

Solution,

We use the slope formula, setting x=a :

`\displaystyle{{{{ \lim_(h \to0)}}} ( (2)/(x + h) - (2)/(x) )/(h) = \lim_(h \to0) ( (2)/(a + h) - (2)/(a) )/(h) }`

`\displaystyle{ \lim_(h \to0) ( (2a - 2(a + h))/(a(a + h)) )/(h) = \displaystyle{ \lim_(h \to0) (2a - 2(a + h))/(ha(a + h)) }}`

`\displaystyle{ \lim_(h \to0) (2a - 2a - 2h)/(ha(a + h)) = \displaystyle{ \lim_(h \to0) ( - 2h)/(ha(a + h)) }}`

`\displaystyle{ \lim_(h \to0) ( - 2)/(a(a + h)) = - \frac{ 2}{ {a}^(2) } }`

Therefore, The slope of the curve y=2/x at x=a is -2/a^2.