Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.6: Analyzing Graphs Of Functions
Problem 6ECP: Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
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plzzzzzzzz help with number #2 only Thank you
![1) Find the hundredth derivative of p (x) = (x + x³ + x")1º (1+ x²)!' (x³ + x³ + x"). Justify your answer.
2\11
2) Use the Chain Rule to express the second derivative of fogin terms of the first and second derivatives of f and g.
3) Show that for any constants M, k, and a, the function
´k(t –
— а)
y(t)
M1+tanh
satisfies the logistic equation:
= kl 1
Note: The function tanh is the hyperbolic tangent function 2: tanh x =
et
- e
2x
1
et
+e-x
2x
+1
4) The lemniscate curve (x2 + y² )² = 4(x² – y²) was discovered by Jacob Bernoulli in 1694, who noted that it is
"shaped like a figure 8, or a knot, or the bow of a ribbon." Find the coordinates of the four points at which the tangent
line is horizontal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1850dea9-ad7a-4b40-bc6a-aa37a68e69da%2Fe722a60a-fad2-4275-b2e4-d23afcc33eab%2F7kuu2mqu_processed.png&w=3840&q=75)
Transcribed Image Text:1) Find the hundredth derivative of p (x) = (x + x³ + x")1º (1+ x²)!' (x³ + x³ + x"). Justify your answer.
2\11
2) Use the Chain Rule to express the second derivative of fogin terms of the first and second derivatives of f and g.
3) Show that for any constants M, k, and a, the function
´k(t –
— а)
y(t)
M1+tanh
satisfies the logistic equation:
= kl 1
Note: The function tanh is the hyperbolic tangent function 2: tanh x =
et
- e
2x
1
et
+e-x
2x
+1
4) The lemniscate curve (x2 + y² )² = 4(x² – y²) was discovered by Jacob Bernoulli in 1694, who noted that it is
"shaped like a figure 8, or a knot, or the bow of a ribbon." Find the coordinates of the four points at which the tangent
line is horizontal.
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