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2 years ago

What is the maximum number of possible extreme values for the function, F(x)=x^3-7x-6

Mathematics

2 answers:

Olin [163]2 years ago

5 0

2 is the max number because it's one less than the degree

notsponge [240]2 years ago

3 0

Answer:

The maximum number of possible extreme values for the function,

$F(x)=x^3-7x-6$ is:

Step-by-step explanation:

By the Theorem of extreme values of a polynomial function we have:

The graph of a polynomial equation of degree n has atmost ( less than or equal to) "n-1" extreme values ( i.e. minima and/or maxima).

That means the total number of extreme values could be n-1, n-3, n-5 etc.

Hence, here we have a polynomial equation as:

$F(x)=x^3-7x-6$

i.e. we have a polynomial function of degree 3 i.e. n=3

So, the maximum number of possible extreme values that may exits is: 2

( Since n-1=3-1=2)

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The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 88/(2 + x2 + y2), where T is measured in °C and x,

-Dominant- [34]

Answer:

$D_uT(3,1)=-\frac{44}{9}*\frac{1}{\sqrt{2} } \approx-3.46$

Step-by-step explanation:

To find the rate of change of temperature with respect to distance at the point (3, 1) in the x-direction and the y-direction we need to find the Directional Derivative of T(x,y). The definition of the directional derivative is given by:

$D_uT(x,y)=T_x(x,y)i+T_y(x,y)j$

Where i and j are the rectangular components of a unit vector. In this case, the problem don't give us additional information, so let's asume:

$i=\frac{1}{\sqrt{2} }$

$j=\frac{1}{\sqrt{2} }$

So, we need to find the partial derivative with respect to x and y:

In order to do the things easier let's make the next substitution:

$u=2+x^2+y^2$

and express T(x,y) as:

$T(x,y)=88*u^{-1}$

The partial derivative with respect to x is:

Using the chain rule:

$\frac{\partial u}{\partial x}=2x$

Hence:

$T_x(x,y)=88*(u^{-2})*\frac{\partial u}{\partial x}$

Symplying the expression and replacing the value of u:

$T_x(x,y)=\frac{-176x}{(2+x^2+y^2)^2}$

The partial derivative with respect to y is:

Using the chain rule:

$\frac{\partial u}{\partial y}=2y$

Hence:

$T_y(x,y)=88*(u^{-2})*\frac{\partial u}{\partial y}$

Symplying the expression and replacing the value of u:

$T_y(x,y)=\frac{-176y}{(2+x^2+y^2)^2}$

Therefore:

$D_uT(x,y)=(\frac{1}{\sqrt{2} } )*(\frac{-176x}{(2+x^2+y^2)^2} -\frac{176y}{(2+x^2+y^2)^2})$

Evaluating the point (3,1)

$D_uT(3,1)=(\frac{1}{\sqrt{2} } )*(\frac{-176(3)-176(1)}{(2+3^2+1^2)^2})=(\frac{1}{\sqrt{2} })* (-\frac{704}{144})=(\frac{1}{\sqrt{2} }) ( - \frac{44}{9})\approx -3.46$

6 0

2 years ago

Amar cycles at a speed of 18km/h.

damaskus [11]

Answer:

<em>The distance between the two villages is 16.5 Km</em>

Step-by-step explanation:

<u>Constant Speed Motion</u>

It's a type of motion in which the distance of an object changes by an equal amount in every equal period of time.

If v is the constant speed, the object travels a distance x in a time t, given by the equation:

x=vt

Amar cycles at v=18 Km/h for t=55 minutes. We need to calculate the distance traveled between the two villages.

Since the speed and the time are given in different units, we convert the time to hours, recalling that 1 hour=60 minute.

t=55 min = 55/60 hours

For the sake of precision, we won't operate the division so far. Compute the distance:

x=18 *55/60=16.5 Km

The distance between the two villages is 16.5 Km

7 0

2 years ago

Which polynomial function could be represented by the graph below?

Svetllana [295]

Note that

$f(x)=x^3+x^2-6x=x(x^2+x-6)=x(x-2)(x+3)$

The x-intercepts are at points x=-3, x=0, x=2. The graph should be increasing - decreasing - increasing.

$f(x)=x^3-x^2-6x=x(x^2-x-6)=x(x+2)(x-3)$

The x-intercepts are at points x=-2, x=0, x=3. The graph should be increasing - decreasing - increasing.

$f(x)=-2x^3-2x^2+12x=-2x(x^2+x-6)=-2x(x-2)(x+3)$

The x-intercepts are at points x=-3, x=0, x=2. The graph should be decreasing - increasing - decreasing.

$f(x)=-2x^3+x^2+12x=-2x(x^2-x-6)=-2x(x+2)(x-3)$

The x-intercepts are at points x=-2, x=0, x=3. The graph should be decreasing - increasing - decreasing.

From the diagram you can see that x-intercepts are at points x=-3, x=0, x=2 and the graph is decreasing-increasing-decreasing.

Answer: correct choice is 3.

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irinina [24]

$0 = 4x^2+2x- 1$

Quadratic formula is

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

'a' is the coefficient of x^2 = 4

'b' is the coefficient of x = 2

'c' is the constant = -1

Now we plug in all the values in quadratic formula

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

$x = \frac{-2+-\sqrt{2^2-4(4)(-1)}}{2(4)}$

$x = \frac{-2+-\sqrt{18}}{8}$

The above one is the substitution of values of a,b,c in quadratic formula.

5 0

2 years ago

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Which graph most likely shows a system of equations with no solutions

Vladimir79 [104]

Answer:

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2 years ago

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