Question

The span of a Astroid is increased along both the x and y axes equally. Then the maximum value of: z = x + y along the Astroid is?

(a) Increases

(b) Decreases

(c) Invariant

(d) The scaling of Astroid is irrelevant

I had been asked this question in final exam.

My doubt is from Lagrange Method of Multiplier to Find Maxima or Minima topic in section Maxima and Minima of Engineering Mathematics

Answer 1

Right option is (a) Increases

Easy explanation: Calculating the gradients considering the general form of Astroid as x^2/3 +  y^2/3 = a^2/3 and then equating them by Lagrange condition.

we can conclude that the maximum value increases.