Math Problem Statement

Please seach for errows

A function is given by f(x) = ax^3 + 5x^2 + 2x + 1, where a is a constant. a) Find f'(x). b) Determine a such that f(1) = -3.

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Polynomials

Formulas

f(x) = ax^3 + 5x^2 + 2x + 1
f'(x) = 3ax^2 + 10x + 2
f(1) = 3a + 11

Theorems

Power Rule for Differentiation

Suitable Grade Level

High School (Grades 11-12)

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