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Find f. f"(x) = −4+ 8x - 12x², f(0) = 4, f'(0) = 12 (Prob. 1,

Find f. f"(x) = −4+ 8x - 12x², f(0) = 4, f'(0) = 12 (Prob. 1,

Calculus: Early Transcendentals
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:** Find the function \( f \). Given: \[ f''(x) = -4 + 8x - 12x^2 \] Conditions: \[ f(0) = 4, \quad f'(0) = 12 \]
Transcribed Image Text:**Problem Statement:** Find the function \( f \). Given: \[ f''(x) = -4 + 8x - 12x^2 \] Conditions: \[ f(0) = 4, \quad f'(0) = 12 \]
Expert Solution
Step 1: Mention the basic integral formulas

Consider the derivative function and initial conditions,

f''x=-4+8x-12x2,f0=4,f'0=12

The objective is to find the function f.

 

Formulas used: ∫xndx=xn+1n+1+C where C is an integral constant.

 

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