First find f' and then find f. f"(x) = 4x − (9x³+x²) + 10, ƒ'(1) = 5, f(1) = -8. ƒ'(x) = f(x) = ← FI

Calculus: Early Transcendentals
8th Edition
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:**

First, find \( f' \) and then find \( f \).

Given the second derivative:
\[ f''(x) = 4x - (9x^3 + x^2) + 10, \]

With initial conditions:
\[ f'(1) = 5, \]
\[ f(1) = -8. \]

**Tasks:**

1. Determine \( f'(x) \).
2. Determine \( f(x) \).

**Solution Steps:**

1. Integrate \( f''(x) \) to find \( f'(x) \).
2. Use the initial condition \( f'(1) = 5 \) to solve for the constant of integration.
3. Integrate \( f'(x) \) to find \( f(x) \).
4. Use the initial condition \( f(1) = -8 \) to solve for the constant of integration in \( f(x) \).
Transcribed Image Text:**Problem Statement:** First, find \( f' \) and then find \( f \). Given the second derivative: \[ f''(x) = 4x - (9x^3 + x^2) + 10, \] With initial conditions: \[ f'(1) = 5, \] \[ f(1) = -8. \] **Tasks:** 1. Determine \( f'(x) \). 2. Determine \( f(x) \). **Solution Steps:** 1. Integrate \( f''(x) \) to find \( f'(x) \). 2. Use the initial condition \( f'(1) = 5 \) to solve for the constant of integration. 3. Integrate \( f'(x) \) to find \( f(x) \). 4. Use the initial condition \( f(1) = -8 \) to solve for the constant of integration in \( f(x) \).
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To find the derivative and the function from its double derivative.

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