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Burka [1]
2 years ago
5

(y − 3)^2 = 4(x − 5), (6, 1). Find an equation of the tangent line to the graph at the given point.

Mathematics
1 answer:
Mandarinka [93]2 years ago
4 0

Answer:

y=x−1. Explanation: (y−3)2=4(x −5). Expanding: y2−6y+9=4x−20. y2−6y−4x=− 29. Differentiating implicitly: 2ydydx−6dydx−4=0.

y=x−1 Explanation: (y−3)2=4(x−5) Expanding: y2−6y+9=4x−20 y2−6y−4x=−29 Differentiating implicitly: 2ydydx−6dydx−4=0 Factor: ... More

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Step-by-step explanation:

1.) First, you need to take the whole numbers (9 and 1) and set them aside.

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3.) Multiply the denominators by each other as well. The denominators are the numbers on the bottom. This will be the denominator of your answer.

4.) Now, you need to multiply your whole numbers (9 and 1) together.

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Your answer will be 9 1/66.

Your work should look like this in the end:

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The points at x equals=​_______ and xequals=​_______ are the inflection points on the normal curve
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We know that the probability density function of a variable that is normally distributed is f(x) = 1/(σ√2π) * exp[1/2 (x – µ). Its inflection point is the point where f"(x) = 0.
Taking the first derivative, we get f'(x) = –(x–µ)/(σ³/√2π) exp[–(x–µ)²/(2σ²)] = –(x–µ) f(x)/σ².
The second derivative would be f"(x) = [ –(x–µ) f(x)/σ]' = –f(x)/σ² – (x–µ) f'(x)/σ² = –f(x)/σ² + (x-µ)² f(x)/σ⁴.
Setting this expression equal to zero, we get
–f(x)/σ² + (x-µ)² f(x)/σ⁴ = 0
Multiply both sides by σ⁴/f(x):
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x = µ +– σ
So the answers are x = µ – σ and x = µ + σ.






8 0
2 years ago
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