Mahagnazk
2021-11-23
Answered

Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results $y=3{x}^{\frac{2}{3}}-2x$

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Luis Sullivan

Answered 2021-11-24
Author has **11** answers

Step 1 Given Function

To Find: Relative extreme, Point of inflection and Asymptotes.

On Sketching the graph of given function we get,

Step 2: From first derivative test definition

Suppose that isa critical point of then

If

If

If f`(x) is the same sign on both sides of

Step 3: On differentiating the given equation we obtain,

Now, to find critical points substitute,

So the critical points obtained

Checking the sign of f`(x)

at each monotone interval we have,

Step 5: By the Inflection point Definition

An inflection point is a point on graph at which the second derivative changes sign

If

IF

Here, We have,

Checking the sign we obtain,

On the Above analysis we find that there are

No any point of Inflection that we have for the given function.

Resulting in No any Vertical as well as Horizontal Asymptotes.

asked 2021-02-05

Use polar coordinates to find the limit. [Hint: Let $x=r\mathrm{cos}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}y=r\mathrm{sin}$ , and note that (x, y) (0, 0) implies r 0.]
$\underset{(x,y)\to (0,0)}{lim}\frac{{x}^{2}-{y}^{2}}{\sqrt{{x}^{2}+{y}^{2}}}$

asked 2021-09-08

There are 100 two-bedroom apartments in the apartment building Lynbrook West.. The montly profit (in dollars) realized from renting out x apartments is given by the following function.

$P\left(x\right)=-12{x}^{2}+2136x-41000$

How many units should be rented out in order to optimize the monthly rental profit?

What is the maximum monthly profit realizable?

asked 2021-09-03

Let $X}_{1},{X}_{2},\dot{s},{X}_{n$ be n independent random variables each with mean 100 and standard deviation 30. Let X be the sum of these random variables. Find n such that Pr$\left(X>2000\right)\ge 0.95$

asked 2021-09-17

Find the complex zeros of the following polynomial function. Write f in factored form.

$f\left(x\right)=2{x}^{4}-5{x}^{3}-20{x}^{2}+115x-52$

The complex zeros of f are ?

The complex zeros of f are ?

asked 2021-11-22

Find the solution set for the system

${x}^{2}+{y}^{2}=25$

$25{x}^{2}+{y}^{2}=25$

by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

asked 2022-01-25

How do you find the critical point and determine whether it is a local maximum, local minimum, or neither for $f(x,y)={x}^{2}+4x+{y}^{2}$ ?

asked 2021-11-22

Graph the sets of points whose polar coordinates satisfy the given polar equation.

The given polar equation is written as follows:

$-\frac{\pi}{2}\le \theta \le \frac{\pi}{2},1\le r\le 2$

The given polar equation is written as follows: