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
lara31 [8.8K]
3 years ago
13

Consider the following. f(x) = x5 − x3 + 6, −1 ≤ x ≤ 1 (a) Use a graph to find the absolute maximum and minimum values of the fu

nction to two decimal places. maximum minimum (b) Use calculus to find the exact maximum and minimum values. maximum minimum

Mathematics
1 answer:
kykrilka [37]3 years ago
4 0

ANSWER

See below

EXPLANATION

Part a)

The given function is

f(x) =  {x}^{5}  -  {x}^{3}  + 6

From the graph, we can observe that, the absolute maximum occurs at (-0.7746,6.1859) and the absolute minimum occurs at (0.7746,5.8141).

b) Using calculus, we find the first derivative of the given function.

f'(x) = 5 {x}^{4} - 3 {x}^{2}

At turning point f'(x)=0.

5 {x}^{4} - 3 {x}^{2}  = 0

This implies that,

{x}^{2} (5 {x}^{2}  - 3) = 0

{x}^{2}  = 0 \: or \: 5 {x}^{2}  - 3 = 0

x =  - \frac{ \sqrt{15} }{5}   \: or \: x = 0 \:  \: or \: x =\frac{ \sqrt{15} }{5}

We plug this values into the original function to obtain the y-values of the turning points

(   -  \frac{ \sqrt{15} }{5}  , \frac{1}{125} ( 6 \sqrt{15}  +750)) \:and \:  (0, - 6) \: and\: (   \frac{ \sqrt{15} }{5}  , \frac{1}{125} ( - 6 \sqrt{15}  +750))

We now use the second derivative test to determine the absolute maximum minimum on the interval [-1,1]

f''(x) = 20 {x}^{3}  - 6x

f''( -  \frac{ \sqrt{15} }{5} ) \:   <  \: 0

Hence

(   -  \frac{ \sqrt{15} }{5}  , \frac{1}{125} ( 6 \sqrt{15}  + 750))

is a maximum point.

f''( \frac{ \sqrt{15} }{5} ) \:    >  \: 0

Hence

(     \frac{ \sqrt{15} }{5}  , \frac{1}{125} (- 6 \sqrt{15}  + 750))

is a minimum point.

f''(0) \: =\: 0

Hence (0,-6) is a point of inflexion

You might be interested in
Donna made a picture frame as a gift for her mom. To make it more stable, she wants to add a brace to the back of it running dia
Komok [63]

Answer:

I think C is the correct answer

4 0
3 years ago
Read 2 more answers
The LCM and the GCF of two numbers is 120 and 8 respectively. If the first number is 24, find the other number​
Ivanshal [37]

Answer: The other no. is 5

Step-by-step explanation: Let the other no. be x

x = LCM/First no.

x = 120/24 = 5

The other no. is 5

7 0
3 years ago
Use the simple interest formula to find the ending balance
IgorC [24]
The answer would be 5,875.00
4 0
3 years ago
PLEASE HELP NOW NOW NOW PLEASE PLEASE HELP
bija089 [108]

Answer:

$46.00

Step-by-step explanation:

$46.00 - $20 + $5 = $21

7 0
3 years ago
the Indian Ocean is 2/10 of the area of the world's oceans. what fraction represents the area of the remaining oceans that make
Shtirlitz [24]
8/10 or 4/5 is what makes up the remaining oceans
4 0
3 years ago
Other questions:
  • Which algebraic expression represents the statement: the product of a number and twelve.
    10·1 answer
  • Need help again imma post about 3 or 3 more pics .
    13·1 answer
  • Write an expression to find the distance (in degrees) between the LATITUDE lines of Moscow and Brasilia. Use absolute value in y
    7·2 answers
  • Three girls each earned $2.55 how much did the three girls earn altogether
    6·2 answers
  • I want help ,i want an answer
    7·1 answer
  • Please give me the correct answer ​
    9·1 answer
  • 8 less a number is less than or equal to 17
    14·2 answers
  • Bao is driving to a concert and needs to pay for parking. There is an automatic fee of
    15·1 answer
  • A student's rectangular desk is 30 inches long and 18 inches wide. The teacher's desk is similar to the student's desk and has a
    11·2 answers
  • Shona bought 5 bags of cement and 4 bags of gravel. The total weight of her bags was 200 kilograms.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!