Question

Please solve all if possible

1. a) Find an equation of the tangent line to the graph of y=x(x+1)^6 at the point where x=−2.

b) [2 points] State the coordinates of the x-intercept of the line.

2. Find f(x) by solving the initial value problem.

f′(x)=2−3x^ −2, f(3)=5.

3. Determine the intervals where the function f(x)=2x^2−1/4x^4 is increasing and decreasing, and also both coordinates of all local extrema, if any. Label each extremum as a maximum or a minimum.

Answer #1

For f(x) xe-x
( a) Find the local extrema by hand using the first derivative
and a sign chart. b) Find the open intervals where the function is
increasing and where it is decreasing. c) Find the intervals of
concavity and inflection points by hand. d) Sketch a reasonable
graph showing all this behavior . Indicate the coordinates of the
local extrema and inflections.

use f(x)=2x^4-4x^2-4 to answer the following.
a) find where f(x) is increasing or decreasing
b) find where f(x) is concave up or down
c) find the coordinates of all relative extrema

a) Find all x- values of the critical values and relative
extrema. Then find
the intervals where the graph is increasing and decreasing.
f(x)= (2/3)x^3+x^2
A) Relative Max: _________________________ B) Relative Min:
__________________________
C) Critical Values: ________________________ D) Increasing
Intervals: ___________________
E) Decreasing Intervals: _____________________
(Please show all work as much as possible)

find the intervals where y is increasing and decreasing as well as
the location of the relative extrema.
y=x^3/2x^2-3x+2

Find all local extrema and the intervals on which
f(x)=x+sin(2x), considered on the interval (-pi/2,pi/2) is
increasing or decreasing.?

1.) Find the equation of the tangent line to the graph of the
function f(x)=5x-4/2x+2 at the point where x=2
2.) Find the derivative: r(t)=(ln(t^3+1))^2

Let f (x) = 3x^4 −4x^3 −12x^2 + 1, deﬁned on R.
(a) Find the intervals where f is increasing, and decreasing.
(b) Find the intervals where f is concave up, and concave
down.
(c) Find the local maxima, the local minima, and the points of
inflection.
(d) Find the Maximum and Minimum Absolute of f over [−2.3]

Suppose that f(x) = (2x)/((4-2x)^3)
Find an equation for the tangent line to the graph of f at
x=1.
Tangent line: y =

Find the intervals on which f(x) is increasing, the intervals
on which f(x) is decreasing, and the local extrema. f(x)=
-2x^2-20x-21

For the function f(x)=x^5+5x^4-4. Write "none" if there isn't an
answer.
(a) find all local extrema of this function, if any, and
increasing and decreasing intervals.
Local max:___ Local min:___ Increasing:___ Decreasing:___
(b) Find all the inflection points of this function, if ay. And
concave up and concave down intervals.
Inflection points:___ concave up:___ concave down:___
(c) Use part a and b to sketch the graph of the function. Must
label important points and show proper concavity.

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