Question

Given the function M(t) = 2t^3 – 3t^2 – 36t, find the critical values and determine, using both the second derivative test and a sign chart, the nature of these critical values.

Answer #1

6. Given vector function r(t) = t2 − 2t, 1 + 3t, 1 3 t 3 + 1 2 t
2 i (a) Find r 0 (t) (b) Find the unit tangent vector to the space
curve of r(t) at t = 3. (c) Find the vector equation of the tangent
line to the curve at t = 3

Given the function f(?) = ?^3 − 9?^2 + 24? − 2,
a) Find the critical numbers and make a sign diagram for the first
derivative.
b) Find the possible inflection points and make a sign diagram for
the second derivative.
c) Using the information to sketch the graph of the function and
show the local mins and maximums and the inflection points on the
graph.

Find the Laplace transform of:
(t^3 - 3t +2)e^(-2t)

Find the average value of the function f(t) = 3t^2 - 2t over the
interval [-1,3].
Show all work please.

Find the length of the curve x = 3t^(2), y = 2t^(3) , 0 ≤ t ≤
1

graph f(t)=t^6-4t^4-2t^3+3t^2+2t on the interval [-3/2,5,2]
using matlab

Differentiate the function. s(t) = 2t − 4(2t^4 + 2)^3
Find the indicated derivative.
dz/dx for z= x^3 + x^2/(1-x-6x^2)

Find the derivative of the parametric curve x=2t-3t2,
y=cos(3t) for 0 ≤ ? ≤ 2?.
Find the values for t where the tangent lines are horizontal on
the parametric curve. For the horizontal tangent lines, you do not
need to find the (x,y) pairs for these values of t.
Find the values for t where the tangent lines are vertical on
the parametric curve. For these values of t find the coordinates of
the points on the parametric curve.

Find an arc length parametrization of r(t)=<3t^2,
2t^3>.
r(g(s))=<_______________, +-____________________>

Find the general solution to y'' - 4y' + 3y = e^t + 3t^2 - 2t +
3

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