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
Fed [463]
3 years ago
14

Let f be a differentiable function such that f(1)=π and f'(x)=√x^3+6. what is the value of f(5)?

Mathematics
1 answer:
natali 33 [55]3 years ago
4 0

The value of f(5) is 49.1

Step-by-step explanation:

To find f(x) from f'(x) use the integration

f(x) = ∫ f'(x)

1. Find The integration of f'(x) with the constant term

2. Substitute x by 1 and f(x) by π to find the constant term

3. Write the differential function f(x) and substitute x by 5 to find f(5)

∵ f'(x) = \sqrt{x^{3}} + 6

- Change the root to fraction power

∵ \sqrt{x^{3}} = x^{\frac{3}{2}}

∴ f'(x) = x^{\frac{3}{2}} + 6

∴ f(x) = ∫ x^{\frac{3}{2}} + 6

- In integration add the power by 1 and divide the coefficient by the

 new power and insert x with the constant term

∴ f(x) = \frac{x^{\frac{5}{2}}}{\frac{5}{2}} + 6x + c

- c is the constant of integration

∵ \frac{x^{\frac{5}{2}}}{\frac{5}{2}}=\frac{2}{5}x^{\frac{5}{2}}

∴ f(x) = \frac{2}{5} x^{\frac{5}{2}} + 6x + c

- To find c substitute x by 1 and f(x) by π

∴ π = \frac{2}{5} (1)^{\frac{5}{2}} + 6(1) + c

∴ π = \frac{2}{5} + 6 + c

∴ π = 6.4 + c

- Subtract 6.4 from both sides

∴ c = - 3.2584

∴ f(x) = \frac{2}{5} x^{\frac{5}{2}} + 6x - 3.2584

To find f(5) Substitute x by 5

∵ x = 5

∴ f(5) = \frac{2}{5} (5)^{\frac{5}{2}} + 6(5) - 3.2584

∴ f(5) = 49.1

The value of f(5) is 49.1

Learn more:

You can learn more about differentiation in brainly.com/question/4279146

#LearnwithBrainly

You might be interested in
How do i factorize x2+14x+49
Fed [463]

Answer:

(x + 7) (x + 7)

Step-by-step explanation:

What's the square root of x^2?

That's x

What's the square root of 49

That's 7

And what makes 14?

7 + 7 = 14

So therefore the answer is (x + 7) (x + 7)

Easy Kevin Durant is so smart!

4 0
2 years ago
Read 2 more answers
N. -2x - 40 = 8(1 -x)​
Irina-Kira [14]

Answer:

x=8

Step-by-step explanation:

−2x−40=8(1−x)

Step 1: Simplify both sides of the equation.

−2x−40=8(1−x)

−2x+−40=(8)(1)+(8)(−x)(Distribute)

−2x+−40=8+−8x

−2x−40=−8x+8

Step 2: Add 8x to both sides.

−2x−40+8x=−8x+8+8x

6x−40=8

Step 3: Add 40 to both sides.

6x−40+40=8+40

6x=48

Step 4: Divide both sides by 6.

\frac{6x}{6} =\frac{48}{6}

to get the answer

x=8

4 0
3 years ago
Thomas invested $1498.00 at 6% simple interest per annum calculate How long it will be before his investment earns $449.40
valentinak56 [21]

Answer:

t = 6 years

Step-by-step explanation:

Use the simple interest formula:  i = prt, where p is the principal, r is the interest rate as a decimal fraction, and is the elapsed time, in years.

Here we want to know how long it will take for the interest alone to reach $449.40.  We first solve i = prt for t, obtaining t = i/(pr).

Here, the length of time is t = ($449.40) / (0.06*$1498.00).  This works out to

t = 5.9947, or approximately 6 years.

t = 6 years

8 0
2 years ago
Is a graph a proportional​
Bogdan [553]

Answer:

How to tell the difference: A proportional graph is a straight line that always goes through the origin. A non-proportional graph is a straight line that does not go through the origin.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Graph the line that passes through the point (0,-7) and (-3,-9) and determine the equation of the line
Blababa [14]

Answer:

The equation is y=2/3x-7

5 0
3 years ago
Read 2 more answers
Other questions:
  • the moon is about 240,00 miles from earth. what is this distance written as a whole number multiplied by a power of ten
    14·1 answer
  • Tickets for an amusement park cost $10 for adults and $6 for children. Find the totaly cost for 2 adults and 3 children. PLS ANS
    12·2 answers
  • Evaluate the expression??<br> 9-5x+2=4-5x
    14·1 answer
  • Describe the pattern in the sequence 13, 15, 17, 19... Then find the next three terms.
    14·1 answer
  • Pleaseeeeee (correct answer pls)
    5·2 answers
  • PLease help will mark brainliest !!!!!
    8·1 answer
  • A side of the triangle below has been extended to form an exterior angle of 151°. Find the value of x.
    12·1 answer
  • Simplify 3 square root 2 - square root 2
    13·1 answer
  • What is the equation of the line that passes through the points (-4,3) and (2,-6)
    10·1 answer
  • 3. Determine the intersection point(s) for the system.<br><br>​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!