1

I have an exam and this has stumped me. I think it is a typo error. So this is part of the question.

a curve of the form $y = Ax^3$, where A is a constant, joining the two endpoints $(1,1)$ and $(2,4)$.

The answer that has been given is $y=\frac{1}{2}x^3$.

Obviously it is just a simple case of inputting the endpoints to get an equation for A. But it leads to two contradicting values of $A$, which leads me to believe that $(1,1)$ should be $(1,1/2)$.

For anyone that is interested in what the question is about, http://www.maths.liv.ac.uk/Past_Exams/PDF_FILES/MATH323-jan08-exam.pdf It is question two.

The answer is supplied here, http://www.maths.liv.ac.uk/Past_Exams/PDF_FILES/MATH323-jan08-soln.pdf

amWhy
  • 209,954
user118282
  • 31

1 Answers1

2

Yes, you are indeed correct that the given endpoints cannot both be correct:

We have $y = Ax^3$

  • $(1, 1):\quad 1 = A$
  • $(2, 4): \quad 4 = 8A\iff A = 1/2$
  • Contradiction

But given the points $(1, \frac 12), (2, 4)$ as endpoints, then indeed, $A = \frac 12$.

amWhy
  • 209,954