Find the second derivative of the function. t° + 10t + 7 d²s 10 14 O A. 715 dt? 13 4 20 42 O B. = 4217 %3D + -+ d?s 10 14 c. = 7t° a?s 20 42 O D. = 42t5 - di?
Find the second derivative of the function. t° + 10t + 7 d²s 10 14 O A. 715 dt? 13 4 20 42 O B. = 4217 %3D + -+ d?s 10 14 c. = 7t° a?s 20 42 O D. = 42t5 - di?
Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem Statement:**
Find the second derivative of the function:
\[
s = \frac{t^9 + 10t + 7}{t^2}
\]
**Options:**
- **A.** \(\frac{d^2s}{dt^2} = 7t^5 - \frac{10}{t^3} - \frac{14}{t^4}\)
- **B.** \(\frac{d^2s}{dt^2} = 42t^7 + \frac{20}{t} + \frac{42}{t^2}\)
- **C.** \(\frac{d^2s}{dt^2} = 7t^6 - \frac{10}{t^2} - \frac{14}{t^3}\)
- **D.** \(\frac{d^2s}{dt^2} = 42t^5 + \frac{20}{t^3} + \frac{42}{t^4}\)
**Explanation:**
This mathematical problem involves finding the second derivative of a given function. The function \(s\) is presented in a rational form, where the numerator is a polynomial \(t^9 + 10t + 7\) and the denominator is \(t^2\).
Candidates need to differentiate this function twice with respect to \(t\) to determine which option (A, B, C, or D) correctly represents the second derivative.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65e9754d-e7bf-4951-a913-18b478a6d2d4%2Fd9cfb570-17ac-4d57-af9b-d88405812abb%2Fiuw7zhw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the second derivative of the function:
\[
s = \frac{t^9 + 10t + 7}{t^2}
\]
**Options:**
- **A.** \(\frac{d^2s}{dt^2} = 7t^5 - \frac{10}{t^3} - \frac{14}{t^4}\)
- **B.** \(\frac{d^2s}{dt^2} = 42t^7 + \frac{20}{t} + \frac{42}{t^2}\)
- **C.** \(\frac{d^2s}{dt^2} = 7t^6 - \frac{10}{t^2} - \frac{14}{t^3}\)
- **D.** \(\frac{d^2s}{dt^2} = 42t^5 + \frac{20}{t^3} + \frac{42}{t^4}\)
**Explanation:**
This mathematical problem involves finding the second derivative of a given function. The function \(s\) is presented in a rational form, where the numerator is a polynomial \(t^9 + 10t + 7\) and the denominator is \(t^2\).
Candidates need to differentiate this function twice with respect to \(t\) to determine which option (A, B, C, or D) correctly represents the second derivative.
Expert Solution
Step 1
We know that ,
d/dt ( tn ) = n tn-1
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