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Ket [755]
3 years ago
10

Determine whether or not the three points are on the same line. (1, -3) (3, 1) (5, 7)

Mathematics
1 answer:
alukav5142 [94]3 years ago
6 0

Answer:

They are on the same line

Step-by-step explanation:

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Find the 2nd Derivative:<br> f(x) = 3x⁴ + 2x² - 8x + 4
ad-work [718]

Answer:

f''(x)=36x^2+4

Step-by-step explanation:

Let's start by finding the first derivative of f(x)= 3x^4+2x^2-8x+4. We can do so by using the power rule for derivatives.

The power rule states that:

  • \frac{d}{dx} (x^n) = n \times x^n^-^1

This means that if you are taking the derivative of a function with powers, you can bring the power down and multiply it with the coefficient, then reduce the power by 1.

Another rule that we need to note is that the derivative of a constant is 0.

Let's apply the power rule to the function f(x).

  • \frac{d}{dx} (3x^4+2x^2-8x+4)

Bring the exponent down and multiply it with the coefficient. Then, reduce the power by 1.

  • \frac{d}{dx} (3x^4+2x^2-8x+4) = ((4)3x^4^-^1+(2)2x^2^-^1-(1)8x^1^-^1+(0)4)

Simplify the equation.

  • \frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x^1-8x^0+0)
  • \frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8(1)+0)
  • \frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8)
  • f'(x)=12x^3+4x-8

Now, this is only the first derivative of the function f(x). Let's find the second derivative by applying the power rule once again, but this time to the first derivative, f'(x).

  • \frac{d}{d} (f'x) = \frac{d}{dx} (12x^3+4x-8)
  • \frac{d}{dx} (12x^3+4x-8) = ((3)12x^3^-^1 + (1)4x^1^-^1 - (0)8)

Simplify the equation.

  • \frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4x^0 - 0)
  • \frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4(1) - 0)
  • \frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4 )

Therefore, this is the 2nd derivative of the function f(x).

We can say that: f''(x)=36x^2+4

6 0
2 years ago
Read 2 more answers
What is the value of f(3) in the function f(x)=5/6x+8
natita [175]

For this case we have a function of the form y = f (x), where f (x) = \frac {5} {6} x + 8

We must find the value of the function when x = 3, that is, we must find f (3). So:

f (3) = \frac {5} {6} (3) + 8\\f (3) = \frac {15} {6} +8\\f (3) = \frac {5} {2} +8\\f (3) = 2.5 + 8\\f (3) = 10.5

Sof (3) = 10.5

Answer:

f (3) = 10.5

3 0
3 years ago
Help........................
GaryK [48]

Answer:

16

Step-by-step explanation:

6 0
2 years ago
if 20 students ride on your bus and two fifth of them pack there lunches how many of them didnt pack there lunch
Vadim26 [7]
Your Answer Is...

12.

(If you need an explanation, comment below.)

Glad I Could Help, And Good Luck!

~AnonymousGiantsFan~
5 0
3 years ago
What are the different ways of the simulation indicates when an equation is balanced?
yKpoI14uk [10]

When an equation is balanced, the different ways that the simulation indicates are as follows:

- Happy Face appears

- The scales are balanced

- Pictures show same kind of atoms in reactants and products

- Pictures show same number of atoms in reactants and products

5 0
3 years ago
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