Mathematics

Problem

Consider the curve specified by

x = t^{2} - 4t + 6

y = t^{3} - 6t^{2} + 9t + 5

, for

t \in \mathbb{R}

. a. Part 1: (i) Derive formulae for

\dfrac{dy}{dx}

and

\dfrac{d^{2}y}{dx^{2}}

in terms of

t

. b. Part 2: (ii) Determine all real values of

t

at which the curve has an inflection point. c. Part 3: (iii) Classify each inflection point found in part (ii) by indicating on which intervals of

t

the curve is concave upward and on which intervals it is concave downward. d. Part 4: (iv) For each inflection point, obtain the corresponding Cartesian coordinates.

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