The radius of a circle is 2 yards. What is the circle's area? r=2 yd Use 3.14 for .

I am having trouble with this relative minimum of this equation.

Norma-Jean [14]

Answer:

So the approximate relative minimum is (0.4,-58.5).

Step-by-step explanation:

Ok this is a calculus approach. You have to let me know if you want this done another way.

Here are some rules I'm going to use:

$(f+g)'=f'+g'$ (Sum rule)

$(cf)'=c(f)'$ (Constant multiple rule)

$(x^n)'=nx^{n-1}$ (Power rule)

$(c)'=0$ (Constant rule)

$(x)'=1$ (Slope of y=x is 1)

$y=4x^3+13x^2-12x-56$

$y'=(4x^3+13x^2-12x-56)'$

$y'=(4x^3)'+(13x^2)'-(12x)'-(56)'$

$y'=4(x^3)'+13(x^2)'-12(x)'-0$

$y'=4(3x^2)+13(2x^1)-12(1)$

$y'=12x^2+26x-12$

Now we set y' equal to 0 and solve for the critical numbers.

$12x^2+26x-12=0$

Divide both sides by 2:

$6x^2+13x-6=0$

Compaer $6x^2+13x-6=0$ to $ax^2+bx+c=0$ to determine the values for $a=6,b=13,c=-6$ .

$a=6$

$b=13$

$c=-6$

We are going to use the quadratic formula to solve for our critical numbers, x.

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}$

$x=\frac{-13 \pm \sqrt{169+144}}{12}$

$x=\frac{-13 \pm \sqrt{313}}{12}$

Let's separate the choices:

$x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}$

Let's approximate both of these:

$x=0.3909838 \text{ or } -2.5576505$ .

This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.

The relative maximum is at approximately -2.5576505.

So the relative minimum is at approximate 0.3909838.

We could also verify this with more calculus of course.

Let's find the second derivative.

$f(x)=4x^3+13x^2-12x-56$

$f'(x)=12x^2+26x-12$

$f''(x)=24x+26$

So if f''(a) is positive then we have a minimum at x=a.

If f''(a) is negative then we have a maximum at x=a.

Rounding to nearest tenths here: x=-2.6 and x=.4

Let's see what f'' gives us at both of these x's.

$24(-2.6)+25$

$-37.5$

So we have a maximum at x=-2.6.

$24(.4)+25$

$9.6+25$

$34.6$

So we have a minimum at x=.4.

Now let's find the corresponding y-value for our relative minimum point since that would complete your question.

We are going to use the equation that relates x and y.

I'm going to use 0.3909838 instead of .4 just so we can be closer to the correct y value.

$y=4(0.3909838)^3+13(0.3909838)^2-12(0.3909838)-56$

I'm shoving this into a calculator:

$y=-58.4654411$

So the approximate relative minimum is (0.4,-58.5).

If you graph $y=4x^3+13x^2-12x-56$ you should see the graph taking a dip at this point.

3 0

3 years ago

State the domain & range!

Simora [160]

Answer:

Domain=x:x is a natural number less than 6: x≠4

Range= x:x is a natural number, 3>=x<=1

8 0

3 years ago

Read 2 more answers

What is 73/50 as a percent

Rainbow [258]

73/50
146/100
146%
The answer would be 146%

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3 years ago

A tennis player moves in a straight-line path as shown in the figure below. find her average velocity in the following time inte

Andreyy89

To find the average velocity in a velocity-time graph at a particular interval, simply determine the gradient at that particular interval.

a. average velocity= 4/1 
= 4m/s 

b. average velocity from 1 to 2.5s= 6/(2.5-1) 
= 4m/s 

average velocity from 2.5 to 4.0s= 0m/s 

average velocity from 0 to 4.0s= (4+0)/4 
= 1m/s 

c. average velocity from 1.0 to 4.0s= (4/3)m/s 

average velocity from 4.0 to 5.0s= 2/1 
= 2.0m/s 

average velocity from 1.0 to 5.0s= ((4/3)+2)/4 
= (5/6)m/s 

d. average velocity from 0 to 4.0s= 1.0m/s 

average velocity from 4.0 to 5.0s= 2.0m/s 

average velocity from 0 to 5.0s= (1.0+2.0)/5 
= (3/5)m/s

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3 years ago

what is 3 to the power of 8 times 3 to the power of 4 divided by 3 to the power of 2 times 3 to the power of 8?

gladu [14]

387420489You can search for any mathematical expression, using functions such as: sin, cos, sqrt, etc. You can find a complete list of functions here.RadDegx!Invsinlnπcoslogetan√AnsEXPxy()%AC789÷456×123−0.=+

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The radius of a circle is 2 yards. What is the circle's area? r=2 yd Use 3.14 for ​.

The radius of a circle is 2 yards. What is the circle's area? r=2 yd Use 3.14 for .