Analyze and sketch a graph of the function. Label any

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=3x232x
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Luis Sullivan
Answered 2021-11-24 Author has 11 answers

Step 1 Given Function
y=3x232x
To Find: Relative extreme, Point of inflection and Asymptotes.
On Sketching the graph of given function we get,
image
Step 2: From first derivative test definition
Suppose that isa critical point of then
If f(x)>0 to the left of x=c and f(x)<0 to the right of x=c then x=c is a local maximum.
If f(x)<0 to the left of x=c and f`(x)>0 to the right of x=c then x=c is a local minimum.
If f`(x) is the same sign on both sides of x=c then x=c is neither a local maximum nor a local local minimum.
Step 3: On differentiating the given equation we obtain,
dydx=3×{23}x132
dydx={2x13}2
Now, to find critical points substitute,
dydx=0
{2x13}2=0
{2x13}=2
x13=1
x=1
So the critical points obtained
x=O and x=1
So the intervals are
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 f(x)>0 then f(x) concave upwards
IF f(x)<0 then f(x) concave downwards
Here, We have,
f(x)=23x43
Checking the sign we obtain,
∝<x<0x=00<x<∝SignNA+BehaviorConcaveDownwardNAConcaveDownward

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.

Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-02-05
Use polar coordinates to find the limit. [Hint: Let x=rcosandy=rsin , and note that (x, y) (0, 0) implies r 0.] lim(x,y)(0,0)x2y2x2+y2
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(x)=12x2+2136x41000 
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 X1,X2,s˙,Xn 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(X>2000)0.95
asked 2021-09-17
Find the complex zeros of the following polynomial function. Write f in factored form.
f(x)=2x45x320x2+115x52
The complex zeros of f are ?
asked 2021-11-22
Find the solution set for the system
x2+y2=25
25x2+y2=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.
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)=x2+4x+y2?
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:
π2θπ2,1r2