1. Find derivative function f'(x).

2. Find the slope of the tangent line using:

m = f'(a)

3. Use the slope-point formula to get the equation of the tangent line:

y - f(a) = m(x-a)

m(t) = -1/m(n)

= (x³ + 4x² + x)' (x + 1) + (x³ + 4x² + x) (x + 1)'

And then find the derivative and calculate it.

= (x³ + 4x² + x)' (x + 1) 3 + (x³ + 4x² + x) (x + 1)' 3 + (x³ + 4x² + x) (x + 1) (3)'

And then find the derivative and calculate it.

= 3 (x³ + 4x² + x)^3-1 (x³ + 4x² + x)'

And then find the derivative and calculate it.

v(t)=s'(t)=h'(t)

Speed function is the absolute value of velocity |v(t)|.

Acceleration function is the derivative of velocity:

a(t)=v'(t)= s"(t) (m/s²)

Jerk function is the derivative of acceleration:

j(t)=a'(t)=v" (t)=s'''(t) (m/s³)