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For the curve `sqrtx+sqrty=1`, what is the value of `(dy)/(dx)` at `((1)/(4),(1)/(4))`?A. `(1)/(2)`B. 1C. `-1`D. 2 |
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Answer» Correct Answer - C Given function : `sqrtx+sqrty=1` is an implicit functionb Differentiating both sides w.r.t. x, we get `(1)/(2sqrtx)+(1)/(2sqrty)(dy)/(dx)=0` `rArr(dy)/(dx)=-sqrt((y)/(x))` Value of `(dy)/(dx)" at "x=(1)/(4),y=(1)/(4)` `((dy)/(dx))_(((1)/(4)","(1)/(4)))=-sqrt((1//4)/(1//4))=-1` |
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