Question

Find the equation of the normal to the curve in y=mx+b format : p(t) = 3t^2 - 8t + 3 at t = 3

Answer 1

Answer:

$y=10x+24$

Step-by-step explanation:

Find the derivative of the function

$p'(t)=\frac{d[p(t)]}{dt}=\frac{d}{dt}(3t^2-8t+3)=6t-8$

Determine the slope of p(t) at t=3:

$p'(3)=6(3)-8=18-8=10$

Find p(3):

$p(3)=3(3)^2-8(3)+3=3(9)-24+3=27-21=6$

Determine y-intercept:

$y=mx+b$

$6=10(3)+b$

$6=30+b$

$-24=b$

Final equation:

$y=10x-24$