Question

For what values of c is there a straight line that intersects
the curve y = x^{4} + cx^{3} + 12x^{2} − 7x
+ 4 in four distinct points? (Enter your answer using interval
notation)

Answer #1

For what values of c is there a straight line that intersects
the curve y=x^4+cx^3+12x^2-2x+8 in 4 distinct points? answer in
interval notation

The
plane y+z=2 intersects the ‘funky’ cylinder x^2 + y^4 =17 in a
curve C.
A) Find a parametric equation of the tangent line to C at the
point (4,1,1)
B) How was the direction vector found in part A and how do you
know its the right direction?

1) Use the First Derivative Test to find the local maximum and
minimum values of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.):
g(u) = 0.3u3 + 1.8u2 + 146
a)
local minimum values:
b)
local maximum values:
2) Consider the following:
f(x) = x4 − 32x2 + 6
(a) Find the intervals on which f is increasing or
decreasing. (Enter your answers using interval notation.)
increasing:
decreasing:...

write a C program to do either a linear (straight
line) or quadratic curve fitting for a set of data points (x,y).
user can choose to enter the data points from the keyboard, or to
read from a file. ( tip: consider least squares fitting technique).
Please draw flow chat & Don't give any graphic methods.

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.)

The line that is normal to the curve X^2+XY-2y^2=0 at (2,2)
intersects the curve what other point

Consider the function below. (If an answer does not exist, enter
DNE.)
g(x) = 250 +
8x3 +
x4
(a) Find the interval of increase. (Enter your answer using
interval notation.)
Find the interval of decrease. (Enter your answer using interval
notation.)
(b) Find the local minimum value(s). (Enter your answers as a
comma-separated list.)
Find the local maximum value(s). (Enter your answers as a
comma-separated list.)
(c) Find the inflection points.
(x, y)=(smaller x-value)
(x, y)=(larger x-value)
Find the...

The folium of descartes is the curve with equation x^3 + y^3 =
3axy where a does not equal 0 and is a constant.
a) Show that for any t not equal to 0, 01 the line y=tx
intersects the folium at the origin and exactly one other point P.
Express the coordinates of P in terms of t to get a
parameterization of the folium.
b) Describe the interval of t-values parameterizing the parts of
the curve in quadrants...

Describe the x-values at which the function is differentiable.
(Enter your answer using interval notation.)
y =
x2
x2 − 9

Consider the equation below. (If an answer does not exist,
enter DNE.)
f(x) = x^4− 50x^2 + 7
(a) Find the interval on which f is increasing. (Enter your
answer using interval notation.)
Find the interval on which f is decreasing. (Enter your answer
using interval notation.)
(b) Find the local minimum and maximum values of f.
local minimum value
local maximum value
(c) Find the inflection points.
(x, y) =
(smaller x-value)
(x, y) =
...

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