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 indicate the sign (+
or -) of dy/dx and of d^{2}y/dx^{2} tabled values.
Reference Power Point Lesson 13 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 (-1.333) and ending X values (1.333) below are not to be
considered critical values. In the space after the instructions for
the “Bonus Opportunity” write the first derivative (dy/dx or Y’).
Set this equal to zero and solve for the X values that make it
equal to zero. Also write the second derivative
(d^{2}y/dx^{2}or Y”)_{.} Set this equal to
zero and solve for the X values that make it equal to zero.
Complete the table by following the example on the cover of the
Assignment 6 folder and/or in Power Point Lesson 13View the scoring
rubric to see how point values are awarded for correct
calculations.

Y = 2X^{3} +2X^{2} -2X -3

X |
-1.333 |
-1 |
-.667 |
-.333 |
0 |
.333 |
.667 |
1.333 |

Y |
||||||||

dy/dx |
||||||||

d |
||||||||

Label Point (MAX, MIN, INF) |

**Twenty point Bonus Opportunity** (creditable
toward the maximum of 1000 points). Use the nine X values and their
Y values you found above (which include the critical values) to
help neatly draw the graph of this polynomial function over the
range of X values given. Alternatively use a
spreadsheet to plot it. Your graph must be consistent with the
tabled values above (which means, if you claim a certain X value is
a maximum, then the graph of it should show this same value as a
maximum. Similarly, if you claim an X value is an inflection point,
then the graph of it should show it to be so. If the derivatives
signal a X value as a minimum, the graph should show the same
minimum, too. The point is, if you figure out how the derivatives
SIGNAL which X values are critical points, the graph of the values
should show them as such. Be certain to indicate these critical
values with labels on the X axis of your graph.

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
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...

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.)

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.

List these six partial derivatives for z = 3 x2 y +
cos (x y) – ex+y
dz/dx dz/dy d2z/dx2 d2z/
dy2 d2z/dxdy d2z/dydx
Evaluate the partial
derivative
dz at the point (2, 3,
30) for the function z = 3 x4 – x y2
dx

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?

Suppose that
f(x)=x−3x^1/3
(A) Find all critical values of f. If there are no critical values,
enter -1000. If there are more than one, enter them separated by
commas.
Critical value(s) =
(B) Use interval notation to indicate where f(x) is
increasing.
Note: When using interval notation in WeBWorK,
you use INF for ∞∞, -INF for
−∞−∞, and U for the union symbol. If there are no
values that satisfy the required condition, then enter "{}" without
the quotation marks....

Consider y = 1 + 3x– 4x3.
a. State the
domain. ____________
b. State the
range. ____________
c. Find the
y-intercept. ____________
d. Find the
x-intercept(s). ____________
e. State the equation of the horizontal
asymptote, if any. ____________
f. State the equation of the slant
asymptote, if
any. ____________
g. State the equation of the vertical
asymptote, if any. ____________
h. State the interval(s) on which the
function is
decreasing. ____________
i. State the interval(s) on which the
function is
increasing. ____________
j. Find
dy/dx. ____________
k. Find the local...

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)

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 15 minutes ago

asked 19 minutes ago

asked 20 minutes ago

asked 22 minutes ago

asked 30 minutes ago

asked 31 minutes ago

asked 34 minutes ago

asked 39 minutes ago

asked 55 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago