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
just olya [345]
2 years ago
5

Question attached and investigates relationship between zeroes and tangents of cubic function

Mathematics
1 answer:
Masja [62]2 years ago
4 0

The tangent lines of the cubic function f(x) = x(x - 2)(x - 6) at the zeros 0, 2 and 6 are y = 12x, y = -8x + 16 and y = 24x - 144

<h3>Part A: The tangent lines of f(x) = x(x - 2)(x - 6)</h3>

The cubic function is given as:

f(x) = x(x - 2)(x - 6)

Expand

f(x) = x³ - 8x² + 12x

Differentiate the function

m = 3x² - 16x + 12

At the point x = 0, we have:

m = 3(0)² - 16(0) + 12

m = 12

Also, we have:

f(0) = 0

A linear equation is represented as:

y = m(x - x₁) + y₁

So, we have:

y = 12(x - 0) + 0

y = 12x

At the point x = 2, we have:

m = 3(2)² - 16(2) + 12

m = -8

Also, we have:

f(2) = 0

A linear equation is represented as:

y = m(x - x₁) + y₁

So, we have:

y = -8(x - 2) + 0

y = -8x + 16

At the point x = 6, we have:

m = 3(6)² - 16(6) + 12

m = 24

Also, we have:

f(6) = 0

A linear equation is represented as:

y = m(x - x₁) + y₁

So, we have:

y = 24(x - 6) + 0

y = 24x - 144

The above means that the tangent lines are:

y = 12x, y = -8x + 16 and y = 24x - 144

From the attached graph, we can see that the tangent lines at the zero values x = 0 and x = 2 intersect the graph of f(x) at the zero value x = 6

<h3>Part B: The tangent lines of f(x) = (x - a)(x - b)(x - c)</h3>

The equation is given as:

f(x) = (x - a)(x - b)(x - c)

To prove the statement using a computer algebra system, simply follow the next steps:

  • Set values for a, b and c
  • Include the following vertices in the plane: (a,f(a)), (b,f(b)) and (c,f(c))
  • Differentiate f(x) i.e g(x) = f'(x)
  • Include the following vertices in the plane: (a,g(a)), (b,g(b)) and (c,g(c))
  • Lastly, plot the following equations: y = g(a)(x - a) + f(a), y = g(b)(x - b) + f(b) and y = g(c)(x - c) + f(c)

See attachment (2) for proof

Read more about tangent lines at:

brainly.com/question/6617153

#SPJ1

You might be interested in
What is Eight less than two cubed, plus twenty divided by five ​
Naddik [55]

Answer:

4, I believe

Step-by-step explanation:

8-8 (2 cubed) + 20 divided by five = 4

4 0
3 years ago
Based on the current eligibility requirement, a study conducted in 2004 showed that federal spending on entitlement programs, pa
slava [35]

Answer:

A) 2.9% of GDP

B) 8.73% of GDP

Step-by-step explanation:

A) To find the rate of spending, let's find the derivative of the function

P(t) = 0.27t² + 1.4t + 2.1 (0 <= t <= 5)

So,

dP/dt = 0.54t + 1.4 which is the annual growth rate.

Since t is measured in decades, thus in 2030 ,it will have been 3 decades, so we have t = 3

So, at t=3; dp/dt = 0.5(3) + 1.4 = 1.5 + 1.4 = 2.9 which means spending in 2030 will be growing at rate of 2.9%

B) The predicated spending is;

P(t) = 0.27t² + 1.4t + 2.1

Thus, in 2030, will be 3 decades so, t= 3

Thus;

P(3) = 0.27(3²) + 1.4(3) + 2.1 = 8.73 which is 8.73% of GDP

5 0
3 years ago
Read 2 more answers
What is the answer to this
IRINA_888 [86]

Answer:  3

Step-by-step explanation:

y-3=2(x+1)

y - 3 = 2x + 2

 +3.        +3

y=2x+5

-1 is the x value so plug it in where the x is in the equation

y=2(-1) +5

y= -2 + 5

y= 3

5 0
3 years ago
Graph a line that contains the point (−6,1) and has a slope of 5
Alexus [3.1K]

Answer:

y=5x+31

Plot points at: (-4,11), (-6,1), (-3, 16)

Step-by-step explanation:

y-1=5(x+6)

y-1=5x+30

y=5x+31

4 0
3 years ago
1-Andrea tenía una deuda de $25 850 en el banco y abonó $18700. ¿Cuál es su deuda<br> actualmente?
lora16 [44]

Answer:

Current debt of Andrea = $7,150

Step-by-step explanation:

Given:

Loan taken by Andrea from bank = $25,850

Amount paid by Andrea to bank = $18,700

Find:

Current debt of Andrea

Computation:

⇒ Current debt of Andrea = Loan taken by Andrea from bank - Amount paid by Andrea to bank

⇒ Current debt of Andrea = 25,850 - 18,700

Current debt of Andrea = $7,150

Note: O information provide about interest.

6 0
3 years ago
Other questions:
  • What substitution should be used to rewrite 16(x3 + 1)2 – 22(x3 + 1) – 3 = 0 as a quadratic equation?
    10·2 answers
  • WILL GIVE BRAINLIEST<br><br> Match the equations of the lines with their graphs
    5·2 answers
  • Donald buy some fabric to make place mats.she needs 1/5 yard of each type of fabric.She has nine different types of fabric to ma
    11·1 answer
  • GEOMETRY How do I do these questions? #6,7,8. Please help thanks!!
    5·1 answer
  • What is the amplitude of y = 4 sin 3x ?
    11·1 answer
  • 1
    14·1 answer
  • X intercept of x+y=5
    14·1 answer
  • Help me please someone i’m stressing out rn :(
    15·1 answer
  • Between which two numbers does the root square 5 lie
    5·1 answer
  • 15 is what percentage of 30
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!