Application of DerivativeHard

Question

The curve y - e^xy + x = 0 has a vertical tangent at

Options

A.(1, 1)

B.(0, 1)

C.(1, 0)

D.no point

Solution

y - e^xy + x = 0
Differentiating w.r.t. to y
1 - e^xy

= 0
= 0
1 - xe^xy = 0
xe^xy = 1 ⇒ x = 1 , y = 0
∴ Point is (1, 0)

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