take derivitive to find slope
[tex]f'(x)=16x-3x^2[/tex]
at x=2
[tex]f'(2)=16(2)-3(2)^2[/tex]
[tex]f'(2)=32-3(4)[/tex]
[tex]f'(2)=32-12[/tex]
[tex]f'(2)=20[/tex]
so the slope of f(x) at the point (2,24) is 20
use point slope form
the equation of a line that passes through the point [tex](x_1,y_1)[/tex] and has a slope of m is
[tex]y-y_1=m(x-x_1)[/tex]
we are given that the slope is 20 and the point is (2,24)
the equation is
[tex]y-24=20(x-2)[/tex]
simplify into different form yourself if needed
