Mathematics

Problem

Consider the curve defined parametrically by

x=3t+2

and

y=2t^{2}-t

. a. (i) Find

\dfrac{dy}{dx}

in terms of

t

. b. (ii) Determine the value(s) of

t

for which the tangent to the curve has slope

5

. c. (iii) Hence find the coordinate(s) of the point(s) on the curve where the tangent has slope

5