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3 years ago

Where do the relative minimum and the relative maximum occur for the unknown function y=f(x)? The only information we have about

the function is: (1) The critical points are x=3 and x=-2, and (2) The second derivative is f''(x)=2x-1

Mathematics

1 answer:

laila [671]3 years ago

7 0

$f''(3)=2\cdot3-1=6-1=5>0 \Rightarrow \text{minimum}\\
f''(-2)=2\cdot(-2)-1=-4-1=-5$

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5b^2+3b-4 how do I find (x,y)?

GrogVix [38]

Answer:

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3 years ago

A function is shown: f(x) = 36x² - 1.

givi [52]

Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)

<h3>What are equivalent functions?</h3>

Equivalent functions are different functions that have equal values when evaluated and compared

<h3>How to determin the equivalent function that best shows the x-intercepts on the graph?</h3>

The function is given as:

f(x) = 36x^2 - 1

Express 1 as 1^2

f(x) = 36x^2 - 1^2

Express 36x^2 as (6x)^2

f(x) = (6x)^2 - 1^2

Apply the difference of two squares.

This is represented as:

(a + b)(a - b) = a^2 - b^2

So, we have the following equation

f(x) = (6x - 1)(6x + 1)

Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)

Read more about equivalent function at:

brainly.com/question/2972832

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8 0

2 years ago

Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7

shtirl [24]

Given:

The focus of the parabola is at (6,-4).

Directrix at y=-7.

To find:

The equation of the parabola.

Solution:

The general equation of a parabola is:

$y=\dfrac{1}{4p}(x-h)^2+k$ ...(i)

Where, (h,k) is vertex, (h,k+p) is the focus and y=k-p is the directrix.

The focus of the parabola is at (6,-4).

$(h,k+p)=(6,-4)$

On comparing both sides, we get

$h=6$

$k+p=-4$ ...(ii)

Directrix at y=-7. So,

$k-p=-7$ ...(iii)

Adding (ii) and (iii), we get

$2k=-11$

$k=\dfrac{-11}{2}$

$k=-5.5$

Putting $k=-5.5$ in (ii), we get

$-5.5+p=-4$

$p=-4+5.5$

$p=1.5$

Putting $h=6, k=-5.5,p=1.5$ in (i), we get

$y=\dfrac{1}{4(1.5)}(x-6)^2+(-5.5)$

$y=\dfrac{1}{6}(x-6)^2-5.5$

Therefore, the equation of the parabola is $y=\dfrac{1}{6}(x-6)^2-5.5$ .

4 0

2 years ago

Solve 9x - 7 = -7 please answer

lawyer [7]

It would be zero bc, 9x-7=-7 you do KCF Change the sign to addition so -7+7=0 now you divide 0 divided by 9=0. Hope this helps

4 0

3 years ago

A shoe manufacturer collected data regarding men's shoe sizes and found that the distribution of sizes exactly fits the normal c

Lina20 [59]

Answer: 97.72%

Step-by-step explanation:

Given : A shoe manufacturer collected data regarding men's shoe sizes and found that the distribution of sizes exactly fits the normal curve.

Let x be the random variable that represents the shoe sizees.

Also, The population mean = $\mu=11$ ; Standard deviation: $\sigma=1.5$

Formula for z:-

$z=\dfrac{x-\mu}{\sigma}$

Put x= 8, we get

$z=\dfrac{8-11}{1.5}=-2$

Now, the probability that the male shoe sizes are greater than 8 :-

$P(x>8)=P(z>-2)=1-P(z\leq-2)\\\\=1-0.0227501=0.9772499\approx0.9772$

Hence, the percent of male shoe sizes are greater than 8 is 97.72%.

7 0

3 years ago