Question

Calculate the Y values corresponding to the X values given
below. Find the critical values for X for the given polynomial by
finding the X values among those given where the first derivative,
dy/dx = 0 and/or X values where the second derivative,
d^{2}y/dx^{2} = 0. Be sure to
find the sign (+ or -) of dy/dx and of
d^{2}y/dx^{2} at all X values. Reference Lesson 13
and the text Appendix A (pp 694 – 698), as needed. Using the first
and second derivative tests with the information you have
calculated, determine which X value(s) represent maximums (MAX),
which minimums (MIN) and which inflection points (INF). Label the
qualifying X value as such. Attach work to convince me you carried
out these calculations. An Excel spreadsheet can make calculations
easier. If used, please attach the spreadsheet file and upload it
with the rest of your work so that I can examine your formulas. The
beginning and ending X values below are not to be considered
critical values. In the space after the “Bonus Opportunity” write
the first derivative (dy/dx) and the second derivative
(d^{2}y/dx^{2}_{)} you used or you will not
receive credit for them.

Y = X^{3} –X^{2} +3

X |
-.333 |
-.25 |
0 |
.25 |
.333 |
.667 |
1 |

Y |
|||||||

dy/dx |
|||||||

d |
|||||||

Label Point (MAX, MIN, INF) |

Answer #1

Calculate the Y values corresponding to the X values given
below. Find the critical values for X for the given polynomial by
finding the X values among those given where the first derivative,
dy/dx = 0 and/or X values where the second derivative,
d2y/dx2 = 0. Be sure to
find the sign (+ or -) of dy/dx and of
d2y/dx2 at all X values. Reference Lesson 13
and the text Appendix A (pp 694 – 698), as needed. Using the...

Calculate the Y values corresponding to the X values given
below. Find the critical values for X for the given polynomial by
finding the X values among those given where the first derivative,
dy/dx = 0 and/or X values where the second derivative,
d2y/dx2 = 0. Be sure to indicate the sign (+
or -) of dy/dx and of d2y/dx2 tabled values.
Reference Power Point Lesson 13 as needed. Using the first and
second derivative tests with the information you...

Find dy/dx and d2y/dx2 for the given parametric curve. For which
values of t is the curve concave upward? x = t3 + 1, y = t2 − t

a)
Find f(x) is f(x) is differentiable everywhere and
f'(x)= { 2x+8, x<2
3x2, x>2
given f(1)=1
b)
the point (-1,2) is on the graph of
y2-x2+2x=5. Approximate the value of y when
x=1.1. Then use dy/dx and
d2y/dx2 to determine if the point (1,-2) is a
max, min, or neither.

Find dy/dx and d2y/dx2.
x = t2 + 6, y = t2
+ 7t
For which values of t is the curve concave upward?
(Enter your answer using interval notation.)

Given the function
h(x)=e^-x^2
Find first derivative f ‘ and second derivative
f''
Find the critical Numbers and determine the intervals
where h(x) is increasing and decreasing.
Find the point of inflection (if it exists) and determine
the intervals where h(x) concaves up and concaves
down.
Find the local Max/Min (including the
y-coordinate)

The curvature at a point P of a curve y =
f(x) is given by the formula below.
k =
|d2y/dx2|
1 + (dy/dx)2
3/2
(a) Use the formula to find the curvature of the parabola
y = x2
at the point
(−2, 4).
(b) At what point does this parabola have maximum curvature?

.Given: f '(x) = x^2 (x-1) (x-2),
a) Find three first order critical values of f(x).
b) Categorize what is happening at each of them (e.g. rel max,
rel min, etc).
c) What is the degree of f(x)?
d) How many infiection points does f(x) have?
2.) Find the absolute max. value of f(x) =2x^3+ 3x^2 - 12x- 1on
the closed interval [0,2]

dy/dx = 2 sqrt(y/x) + y/x (x<0)
Find general solution of the given ODE

Suppose that
f(x)=4x2ln(x),x>0.f(x)=4x2ln(x),x>0.
(A) List all the critical values of f(x)f(x). Note: If there are
no critical values, enter 'NONE'.
(B) Use interval notation to indicate where f(x)f(x) is
increasing.
Note: Use 'INF' for ∞∞, '-INF' for −∞−∞, and use
'U' for the union symbol. If there is no interval, enter
'NONE'.
Increasing:
(C) Use interval notation to indicate where f(x)f(x) is
decreasing.
Decreasing:
(D) List the xx values of all local maxima of f(x)f(x). If there
are no local...

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