Question

Find the equation of the osculating circle at the local minimum of f(x)=3x^3−5x^2+(0/1)x+5

Answer #1

Find the equation of the osculating circle at the local minimum
of: f(x) = 3x^2 - 7x^2 + 40x/9 + 7

consider the function
f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and
f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) find the local maximum and minimum values. Justify your
answer using the first or second derivative test . round your
answers to the nearest tenth as needed.
b)find the intervals of concavity and any inflection points of
f. Round to the nearest tenth as needed.
c)graph f(x) and label each important part (domain, x- and y-
intercepts, VA/HA, CN, Increasing/decreasing, local min/max values,
intervals of concavity/ inflection points of f?

Find the equation of the osculating
circle of the parabola y =
x^2 at the
origin.

(1 point) The function f(x)=3x+5x^−1 has one local minimum and
one local maximum.
This function has a local maximum at x= _____with value______
and a local minimum at x= ______with value_____

Differentiate
f(x) = (√ x +1)(x(2/5)+3x)
f(x) =(5x3+1)/(x2+2x+1)
f(x) = -5x(3x-3)4
f(x) = (2x +
(x2+x)4)(1/3)

5. Part I
If f(x) = 2x 2 - 3x + 1, find f(3) - f(2).
A. 0
B. 7
C. 17
Part II
If G( x ) = 5 x - 2, find G-1(x).
A. -5x + 2
B. (x + 2)/5
C. (x/5) + 2
Please help me solve this problem and if you can please also
show or explain how you got that answer. Thank you! :)

consider the funtion f(x)=3x-5/sqrt x^2+1. given
f'(x)=5x+3/(x^2+1)^3/2 and f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) Find the domain of f. (write in interval notation):
Df:=_____________?
b) Find the x- and y- intercepts. if any. (write your answers as
ordered pairs).
c) Find the asymptotes of f, if any. If there are not, write
why. (write answers as equations).
d) Find all of the critical numbers of f. on what intervals is f
increasing/decreasing?
show all work

f(x) = −x^2 + 5x and g(x) = 3x − 3 Find the area of the region
completely enclosed by the graphs of the given functions f and
g.

1. Let f(x)=−x^2+13x+4
a.Find the derivative f '(x)
b. Find f '(−3)
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded
to 2 decimal places.
f '(3)=
3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x).
f '(x)=
4. Find the derivative of the function f(x)=√x−5/x^4
f '(x)=
5. Find the derivative of the function f(x)=2x−5/3x−3
f '(x)=
6. Find the derivative of the function
g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your
answer.
g '(x)=
7. Let f(x)=(−x^2+x+3)^5
a. Find the derivative....

1.Let y=6x^2. Find a parametrization of the
osculating circle at the point x=4.
2. Find the vector OQ−→− to the center of the
osculating circle, and its radius R at the point
indicated. r⃗
(t)=<2t−sin(t),
1−cos(t)>,t=π
3. Find the unit normal vector N⃗ (t)
of r⃗ (t)=<10t^2, 2t^3>
at t=1.
4. Find the normal vector to r⃗
(t)=<3⋅t,3⋅cos(t)> at
t=π4.
5. Evaluate the curvature of r⃗
(t)=<3−12t, e^(2t−24),
24t−t2> at the point t=12.
6. Calculate the curvature function for r⃗...

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