3.34: Curve sketch; Jess AP and Kyle GP running

Find the coordinates of the stationary points on the given cubic/product curve, in exact form.

Sketch the graph, stating axis intercepts.

Write down $k$ such that the equation equals $k$ has exactly $3$ distinct solutions.

Jess runs $2$, $2.5$, $3,\ldots$ km each week. Find the week in which each run is $16$ km.

Find the total distance by the end of week $8$.

Kyle's weekly distances $2$, $2.5$, $3.125,\ldots$ form a GP. Find $r$.

Find the first week in which Kyle runs more than $16$ km each day.

Find Kyle's total distance by the end of week $8$.