find the critical points of the following function.\n\nf(x)=3x^{2}+5x + 1\n\nwhat is the derivative of…

find the critical points of the following function.\n\nf(x)=3x^{2}+5x + 1\n\nwhat is the derivative of f(x)=3x^{2}+5x + 1?\n\nf(x)=\\square

find the critical points of the following function.\n\nf(x)=3x^{2}+5x + 1\n\nwhat is the derivative of f(x)=3x^{2}+5x + 1?\n\nf(x)=\\square

Answer

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)