Answer:
[tex]y=10x+24[/tex]
Step-by-step explanation:
Find the derivative of the function
[tex]p'(t)=\frac{d[p(t)]}{dt}=\frac{d}{dt}(3t^2-8t+3)=6t-8[/tex]
Determine the slope of p(t) at t=3:
[tex]p'(3)=6(3)-8=18-8=10[/tex]
Find p(3):
[tex]p(3)=3(3)^2-8(3)+3=3(9)-24+3=27-21=6[/tex]
Determine y-intercept:
[tex]y=mx+b[/tex]
[tex]6=10(3)+b[/tex]
[tex]6=30+b[/tex]
[tex]-24=b[/tex]
Final equation:
[tex]y=10x-24[/tex]
