1/3y=3<br> Find the value of y

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

Which equations have the same pair of solutions? Select all that apply. n(n + 3)(n - 4) = 0 2n(4n + 6)(6n - 4) = 0 0 = 2n(6 - 4n

Zina [86]

Answer:

2, 4, 5, and 6 have the same pair of solutions.

Step-by-step explanation:

1. n(n+3)(n-4) = 0

2. 2n(4n+6)(6n-4) = 0

3. 2n(6-4n)(4n-6n) = 0

4. n(2n+3)(3n-2) = 0

5. 2n(2n+3)(3n-2) = 0

6. 3n(6n+9)(9n-6) = 0

Answers:

1. n = 0, -3, 4

2. n = 0, -3/2, 2/3

3. n = 0, 3/2

4. n = 0, -3/2, 2/3

5. n = 0, -3/2, 2/3

6. n = 0, -3/2, 2/3

8 0

4 years ago

Read 2 more answers

Which of these strategies would eliminate a variable in the system of equations?

valentinak56 [21]

8x+8y=2
-) 8x+5y=1
——————
3y=1
y=1/3
8x+8(1/3)=2
24x+8=6
24x=-2
x=-1/12
(-1/12,1/3)

4 0

3 years ago

Read 2 more answers

Please help! Don't put anything random for the points I really need help!

Kamila [148]

Answer:

x = -2 and x = 5/4

Step-by-step explanation:

The image below shows step-by-step on how to solve it.

Hope this helps! :)

8 0

3 years ago

If anyone would be able to help me. it would be great.

Triss [41]

65% = 156

1% = 165 ÷ 65
1% = $2.40

100% = 2.4 x 100
100% = $240

Answer: The original price 20 years ago was $240.

240 - 156 = $84

Answer: The current price is $84.

3 0

4 years ago

1/3y=3 Find the value of y