Home › Previous year questions › GATE 2020 ST › Question 40GATE 2020 ST – Question 40 Calculus · Multivariable Calculus · 2 marks · Multiple choice
For $f(x,y)=|y-2|\sqrt{|x-1|}$, which is true?
f is differentiable at(1,2). f is continuous but not differentiable there. Its x partial derivative there does not exist. Its derivative in direction(1/√2,1/√2) is1. Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (A) f is differentiable at(1,2).
Explanation At the point both coordinate partials are zero. Set h=x−1,k=y−2 and r=√(h²+k²). Then |f|/r=|k|√|h|/r≤√r→0. Thus the zero linear map is the derivative, A; the product vanishes fast enough despite each factor’s separate cusp.
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