Given: $f(x)=2x^3-5x^2-4x+3$

$11$ Neatly draw the graph of $f$ on the given graph paper in ANNEXURE A$.$ Clearly indicate all intercepts with the axes and coordinates of turning points.

$1\mathrm{.}2$ Determine the first derivative of $f$ and call it $g.$

$13$ Draw the graph of $g$ on the same system of axes as $f$ in ANNEXURE A$.$ Clearly indicate all intercepts with the axes and coordinates of turning points.

$1\mathrm{.}4$ Determine the second derivative of $f$ and call it $h.$ Then sketch the graph of $h$ on the same system of axes as $f$ and $g$ in ANNEXURE A$.$ Clearly indicate all intercepts with the axes.

$1\mathrm{.}5$ What do you notice about the $x-$intercepts of the quadratic function and the $x-$coordinates of the turning points of the cubic function?

$1\mathrm{.}6$ The inflection point can be determined by firstly solving $f^{\text{'}\text{'}}(x)=0.$ It can also be determined by calculating the midpoint between the turning points of the cubic graph.

Hence determine the inflection point of $f.$

$1\mathrm{.}7$ What do you notice about the axis of symmetry of $g,$ the $x-$intercept of $h$ and the $x-$coordinate of the inflection point of $f?$