**Problem**

**Introduction**

This is a Additional Mathematics textbook problem. This question is of an intermediate level of
difficulty. The general method is by

*differentiation*. The equation of the curve happens to be capable of being put into a quadratic equation in*x*. Hence we can also use the theory of*quadratic discriminants*. I present both methods of solution.

__Method 1__**(Using differential calculus)**

__Method 2__**(Using quadratic discriminants)**

**Heuristics Used**

H04. Look for
pattern(s)

H05. Work backwards

H09. Restate the
problem in another way

H11. Solve part of
the problem

H12* Think of a
related problem

H13* Use Equation /
write a Mathematical Sentence

**Suitable Levels**

*****GCE ‘O’ Level Additional Mathematics

* other syllabuses that involve differentiation
or quadratic discriminants

* any independent learner who is interested
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