College Math Placement Practice Test 2025 - Free College Math Questions and Study Guide

Question: 1 / 400

What is the derivative of the function f(x) = x² + 3x - 5?

f'(x) = 3x + 2

f'(x) = 2x + 3

To find the derivative of the function \( f(x) = x^2 + 3x - 5 \), we apply the rules of differentiation for each term in the polynomial.

1. The first term is \( x^2 \). The derivative of \( x^n \) is \( n \cdot x^{n-1} \); thus, for \( x^2 \), the derivative is \( 2x^{2-1} = 2x \).

2. The second term is \( 3x \). The derivative of a constant multiplied by a variable is simply the constant itself, resulting in \( 3 \).

3. The last term is \( -5 \). The derivative of a constant is always zero, so the derivative of \( -5 \) is \( 0 \).

Now, combining these results, the derivative of the function \( f(x) \) is:

\[

f'(x) = 2x + 3 + 0 = 2x + 3.

\]

This shows that the correct answer to the derivative of the function is \( f'(x) = 2x + 3 \), which corresponds to the choice provided. Understanding how to

Get further explanation with Examzify DeepDiveBeta

f'(x) = x + 3

f'(x) = 2x - 3

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