Question

find the critical points of the following function.

f(x)=3x^{2}+5x + 1

what is the derivative of f(x)=3x^{2}+5x + 1?

f(x)=\square

Explanation:

Step1: Apply power rule

The power rule states that if \(y = ax^{n}\), then \(y^\prime=anx^{n - 1}\). For \(f(x)=3x^{2}+5x + 1\), the derivative of \(3x^{2}\) is \(3\times2x^{2-1}=6x\), the derivative of \(5x\) is \(5\times1x^{1 - 1}=5\), and the derivative of the constant \(1\) is \(0\).

Step2: Combine the derivatives

\(f^\prime(x)=(3x^{2})^\prime+(5x)^\prime+(1)^\prime\)
\(f^\prime(x)=6x + 5+0\)

Answer:

\(6x + 5\)