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2 years ago

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Which functions are continuous at x= -5? Select all that apply.

2 answers:

katrin2010 [14]2 years ago

5 0

Answer:

The correct ones i belive are B and C

Assoli18 [71]2 years ago

3 0

Answer:

option B and C

Step-by-step explanation:

Lets check each function

Lets simplify $\frac{x^2-25}{x+5}$

factor the numerator

$x^2-25 = (x+5)(x-5)$

$\frac{(x+5)(x-5}{x+5}$

Cancel out x+5 so we are left with x-5

When x=-5 then f(x) = x-5= -5-5 = -10

To make the function continuous at x=-5 the value of f(x) should be -10

So option B is correct

Now we check with option C and D

Lets simplify $\frac{x^2+10x+25}{x+5}$

factor the numerator

$x^2+10x+25 = (x+5)(x+5)$

$\frac{(x+5)(x-5}{x+5}$

Cancel out x+5 , so we are left with x+5

When x=-5 then f(x) = x+5= -5+5 = 0

To make the function continuous at x=-5 the value of f(x) should be 0

So option C is correct

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I am having trouble with this relative minimum of this equation.<br>

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.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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-21 – (-14) =+=<br> Helpppp

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Answer:

-21 - (-14) = <u>-21</u> + <u>14</u> = <u>-7</u>

Step-by-step explanation:

A - and a - make a +. So -21 - (-14) makes -21 + 14. Solve to get -7.

Hope it helps!

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elena-14-01-66 [18.8K]

Answer:

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Step-by-step explanations:

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2 years ago