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Nitella [24]
3 years ago
14

Find the critical point of the function f(x) = x2 + 2x - 3.

Mathematics
1 answer:
gogolik [260]3 years ago
8 0

Answer:

(-1, -4)

Step-by-step explanation:

The critical point is the point where the slope is 0 or undefined.

This is a parabola (quadratic), so there wont be any undefined points, only a critical point where slope is 0.

We need to take the derivative of the function and set it equal to 0 to find the x coordinate of the critical point. Then we plug in that x point into original equation to find the y coordinate.

Lets see the power rule of differentiation before we differentiate this function.

Power Rule:  \frac{d}{dx}(x^n)=nx^{n-1}

Also, differentiation a constant is always 0!!

Now, differentiating:

f(x)=x^2+2x-3\\\frac{d}{dx}(f(x))=2x+2

Now, we set equal to 0 and find x:

2x+2=0\\2x=-2\\x=\frac{-2}{2}\\x=-1

Now, we find y:

f(x=-1)=(-1)^2+2(-1)-3=-4

So,

x = -1

y = -4

<u>The critical point is  (-1, -4)</u>

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A recipe for fruit punch calls for every 9 cups of grapefruit juice for every 4 cups of OJ. If 60 cups of OJ are used, then how
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2 years ago
Please someone help me with this please. Thank you.
scoundrel [369]

Answer:

f(x)=2+3x

f(x)=1+2x

f(x)=3+4x

Step-by-step explanation:

(Refer to picture)

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5 0
3 years ago
The square root of -1 is:
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The square root of -1 is I
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3 years ago
Hello everyone, could you please solve this problem step by step. I don't have the exact solution and there are no options for i
lara31 [8.8K]

Answer:

<em>The area of the shaded part  = 61.46</em>

<em />

Step-by-step explanation:

Assume the hypotenuse of the triangle is c (c>0)

As the triangle inscribed in the semi circle is the right angle triangle, its hypotenuse is equal to the diameter of the circle.

The hypotenuse of the triangle can be calculated by Pythagoras theorem as following: c^{2} =a^{2} +b^{2} =(2\sqrt{5}) ^{2} + (4\sqrt{5}) ^{2} = 20 + 80 = 100

=> c = 10

So that the semi circle has the diameter = 10 => its radius = 5

  • The total area of 2 semi circles is equal to the area of the circle with radius =5

    => The total area of 2 semi circles is: \pi x 5^{2} = 25\pi

  • The area of a triangle inscribed in the semi circle is: 1/2 x a x b = 1/2 x 2\sqrt{5\\ x 4\sqrt{5} = 20

    => The area of 2 triangles inscribed in 2 semi circles is: 2 x 20 = 40

  • The area of the square is: c^{2} = 10^{2} =100

It can be seen that:

<em>The area of the shaded part = The area of the square - The total area of 2 semi circles + The total are of 2 triangles inscribed in semi circles </em>

<em>= 100 -  25</em>\pi<em> + 40 = 61.46</em>

6 0
2 years ago
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