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3 years ago

What is f(x)? What point is on the graph of f?

Mathematics

1 answer:

max2010maxim [7]3 years ago

6 0

Answer: A) -2; (2, -2)

Step-by-step explanation: If x is 2 then only the first two answers have the possibilty of being correct since in the coordinate pair the x coordinate is 2.

Sub in x and solve equation

$\frac{x^2-2}{x-3}\\\frac{2^2-2}{2-3}\\\frac{4-2}{-1} \\\frac{2}{-1} \\-2$

f(x)=-2 so that is where the point of f is.

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F(x) = 4x +11; [-6, 0]<br> The domain of f(x) is

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3 years ago

What number has a place value of that is 100 times the place value of 6 in 2,386?

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3 years ago

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3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

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2 years ago

the ratio of isabella money to shane money is 3:11 if isabella has 33$ how much money do shane and isabella have together use di

Liono4ka [1.6K]

Together both shane and isabella have 42$

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3 years ago

Hi thank you for helping me

svetlana [45]

Answer:

Step-by-step explanation:

4 + 2x < 6 + 6x

4 - 4x < 6

-4x < 2

x > -1/2

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3 years ago

Read 2 more answers