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grandymaker [24]
3 years ago
8

Multivariable Calculus Question:

Mathematics
1 answer:
vovangra [49]3 years ago
3 0
f(2,-1)=2^2-(-1)^2=3

so we're considering the level curve

x^2-y^2=3

The tangent line to this curve at (2, -1) will be the value of \dfrac{\mathrm dy}{\mathrm dx} at this point. Differentiating yields

2x-2y\dfrac{\mathrm dy}{\mathrm dx}=0\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac xy

and so the slope of the tangent would be \dfrac2{-1}=-2.

The tangent line then has equation

y-(-1)=-2(x-2)\implies y=-2x+3
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