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
Hatshy [7]
3 years ago
13

Consider the function f(x) = 6sin(x^2) on the interval 0 ≤ x ≤ 3.

Mathematics
2 answers:
Vitek1552 [10]3 years ago
4 0
<span> a) F' = 6 sin(x^2) = 0
x^2 = pi
x = sqrt(pi)

b) Fmax = F(1) + integral [1, pi] f(x) dx = 9.7743 </span>
stira [4]3 years ago
4 0

Solution:

The given function is

f(x)= 6 sin x²→→→0 ≤ x ≤ 3.

Differentiating once

f'(x)= 6 cos x²× 2 x=12 x cos x²

For Maximum or Minimum

f'(x)=0

12 x cos x²=0

cos x²=0 ∧ x=0

cos x²=cos \frac{\pi }{2}

x²=  \frac{\pi}{2}

x= \pm \sqrt\frac{\pi}{2}

As, the interval given is,  0 ≤ x ≤ 3.

x=  \sqrt\frac{\pi}{2}= \frac{22}{14}

f"(x)=12 (-sin x²) × 2 x × x + 12 cos x²= 24 x². (-sin x²)+ 12 cos x²

At, x=  \sqrt\frac{\pi}{2}= \frac{22}{14}

f"(x)=-24 × \frac{\pi}{2} ×1 + 0= A negative number

Showing the function attains maxima at this point.

f(0)=6 sin 0=0

f(3)= 6 sin 3²= 6 sin 9(radian)=6 × 0.40(approx)= 2.40

f( \sqrt\frac{\pi}{2})=6 × sin(\frac{\pi}{2} )= 6 ×1=6→→Maximum Value

(b) f(1)=5

I.e at x=1, y=5

Maximum value attained by , f(x)=6 sin x² is 6 at , x=  \sqrt\frac{\pi}{2}.


You might be interested in
A man that is 6 feet tall is standing so that the tip of his shadow is 20 feet from a light pole. His shadow is 8 feet long. Wha
Ksju [112]

Answer:

15 feet

Step-by-step explanation:

4 0
3 years ago
PLEASEE HELP!!<br><br> Write and equation for this graph in slope- intercept form.
ella [17]
-2/1. You find two point that go on the line and if it’s going down it’s negative
8 0
2 years ago
Read 2 more answers
Which phrase best describes the translation from the group y=2x^2 to the graph of y= 2x^2 +5
dsp73

Answer:

The graph move up 5.

Step-by-step explanation:

When we add a constant to the end of a parabola, it shifts the graph up and down. Since the constant here is positive, the graph moves up by that number (5)

7 0
3 years ago
Which table represents a linear function?<br> PLEASE HELP ME
-Dominant- [34]

Answer:

Bottom left

Step-by-step explanation:

If you graph out the coordinates it goes in a perfect line, thus being linear.

6 0
2 years ago
betty has 15 less than triple the number of points that jennie has. Write an expression to find how many points betty 1. has??
Troyanec [42]
3x - 15

less than or more than trick-------> the number before those words should be the second number in the equation
4 0
3 years ago
Read 2 more answers
Other questions:
  • You invested $1,400 in an account that pays 5 percent simple interest. how much more could you have earned over a 20-year period
    10·1 answer
  • The equation of a circle centered at the origin is x^2+y^2=64.what is the radius of the circle?
    13·2 answers
  • Find the value of X.
    11·1 answer
  • What quantity will correctly complete the formula? arc length = ?/360circumference
    13·1 answer
  • In a geometric sequence, the ratio between consecutive terms is _____ constant?
    5·2 answers
  • Francine is making a necklace that has 1 blue Bead for every 6 white beads how many white beads with she use if she uses 11 blue
    8·2 answers
  • A bag contains 3 red marbles, 4 blue, 9 yellow, and 5 green. What is the probability of getting a yellow or a green?
    14·1 answer
  • What is a unit fraction of 4/5
    5·1 answer
  • Pls help me in math pls the question : the time on this clock as minutes to?​
    13·2 answers
  • Or
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!