1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Westkost [7]
2 years ago
8

Find a and b so that f(x) = x^3 + ax^2 + b will have a critical point at (2,3).

Mathematics
1 answer:
Digiron [165]2 years ago
4 0

Using the critical point concept, it is found that a = -3 and b = 7.

<h3>What are the critical points of a function?</h3>
  • The critical points of a function are the values of x for which:

f^{\prime}(x) = 0

In this problem, the function is:

f(x) = x^3 + ax^2 + b

Hence, the derivative is:

f^{\prime}(x) = 3x^2 + 2ax

Then:

f^{\prime}(x) = 0

3x^2 + 2ax = 0

x(3x + 2a) = 0

x = 0

3x + 2a = 0

3x = -2a

x = -\frac{2a}{3}

Since the critical point is at x = 2, we have that:

-\frac{2a}{3} = 2

-2a = 6

2a = -6

a = -3

Then:

f(x) = x^3 - 3x^2 + b

Critical point at (2,3) means that when x = 2, y = 3, then:

3 = 2^3 - 3(2)^2 + b

8 - 12 + b = 3

b = 7

You can learn more about the critical point concept at brainly.com/question/2256078

You might be interested in
Whats the answer to this problem
vlabodo [156]
The answer would be to the right since after you factor the equation out the 9 is positive
8 0
3 years ago
What is 38 in denary in base 8
Naily [24]
First divide by 8:_

38 / 8 = 4  remainder 6

so its 46
4 0
3 years ago
If 15% of an item is $18.00 what was the original price?
larisa [96]
<span>from the whole price,
15% of this price is equal to $18.00.
therefore if 15 % equals $18.00
                                                                     
then 100% is the original price therefore 100 % = 18.00 / 15 % x 100% = $120 therefore original price = $120</span>
5 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=2x-y%3D4%5C%5Cy-x%3D4" id="TexFormula1" title="2x-y=4\\y-x=4" alt="2x-y=4\\y-x=4" align="absmi
Flura [38]
Here is the answer. Hope this helps!

5 0
2 years ago
What is the y-intercept of the line?<br><br> y= -2x - 8<br><br> y-intercept =
ivolga24 [154]

Like I said on the other question. Slope will ALWAYS be the number beside x and y-intercept will always be after that.

Slope-intercept form = y = mx + b

Slope goes where m is and y-intercept goes where b is.

Hope this helps!

3 0
3 years ago
Read 2 more answers
Other questions:
  • Which value of b will make the system y=2x+2 and y=2.5x+b intersect at the point (2,6)
    5·1 answer
  • When students at Luray Middle School were surveyed, 22% said they would like hamburgers at lunch rather than hotdogs. What is th
    9·2 answers
  • Find the value of x. 6+3x and x+14?
    5·2 answers
  • Simplify 2(x + y) + 3(x + y). <br> 2xy + 3xy <br> 5xy <br> 5x + 5y
    11·2 answers
  • Identify the features of the graph
    15·1 answer
  • What is the solution to the equation -(5-(a+1))=9-(5-(2a-3))
    15·2 answers
  • What's the distance between the points (4,3) and (16,8)
    14·2 answers
  • Need help on this please
    5·2 answers
  • Beth writes a number that shows 60 parts out of 100
    5·2 answers
  • Dale has a special deck of cards. Each card has a different rational number on it. The cards are 0.25, 4/5, 2/9, 0.48, and 8/11.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!