All categories

2 years ago

Identify the vertex, axis of symmetry, direction of opening, min/max value, y-intercept, and x-intercepts of this equation:

1 answer:

5 0

(-3/2, 27\4) is the vertex it opens down max at the vertex mins are negative infiity x intercepts at -1 and 3 y intercept at (0,0)

You might be interested in

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

URGENT<br><br>What is the value of x?

oksano4ka [1.4K]

Answer:

Step-by-step explanation: miane

Sumida

8 0

2 years ago

Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for

UkoKoshka [18]

I need sum more info just email me and we can get this dun

8 0

2 years ago

Help!!! What is the slop of the line??

sergiy2304 [10]

I believe it is negative 2/2, hope this helps you out.

8 0

2 years ago

Read 2 more answers

How will a high outlier in a data set affect the mean and median?

RUDIKE [14]

Answer:

B. distribution skewed to the right, mean pulled to the right, median not effected

Step-by-step explanation:

When a distribution is skewed to the right, it means that the data is positively skewed or has more positive numbers than negative numbers.

An outlier can affect the mean of a distribution since a high value outlier will make the mean be much higher than the median. In this case, since the distribution is positively skewed, a high outlier will pull the mean to the right (to higher positive values).

5 0

2 years ago