How to find equation of tangent line using implicit differentiation

Asked by admin @ 26/11/2021 in Mathematics viewed by 315 People

Calculus Questions using implicit differentiation to find the equation of the tangent line that is given curve at the 2, -1

Answered by admin @ 26/11/2021

The tangent line to the curve has slope equal to $\frac{\mathrm dy}{\mathrm dx}$ at the point (2, -1). We have, by implicit differentiation,

$3y^2-6xy=2x+11\implies6y\dfrac{\mathrm dy}{\mathrm dx}-6y-6x\dfrac{\mathrm dy}{\mathrm dx}=2$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2+6y}{6y-6x}=\dfrac{1+3y}{3y-3x}$

At the point (2, -1), the slope is then 2/9, so the tangent line has equation

$y-(-1)=\dfrac29(x-2)\implies y=\dfrac29x-\dfrac{13}9$

Find the equation of the tangent line at the point

Asked by admin @ 11/11/2021 in Mathematics viewed by 299 persons

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Asked by admin @ 29/10/2021 in Mathematics viewed by 306 persons

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Asked by admin @ 29/10/2021 in Mathematics viewed by 294 persons

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Asked by admin @ 17/08/2021 in Math viewed by 308 persons

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Asked by admin @ 22/11/2021 in Mathematics viewed by 344 persons

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Asked by admin @ 09/11/2021 in Mathematics viewed by 356 persons

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Asked by admin @ 09/11/2021 in Mathematics viewed by 361 persons

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Asked by admin @ 07/11/2021 in Mathematics viewed by 355 persons

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Asked by maham237 @ 26/12/2020 in Mathematics viewed by 385 persons

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Asked by maham237 @ 25/12/2020 in Mathematics viewed by 312 persons

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