Question

find the critical points of the following function.
f(x)=3x² + 5x + 1
what is the derivative of f(x)=3x² + 5x + 1?
f(x)=6x + 5
find the critical points, if any, of f on the domain. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the critical point(s) occur(s) at x=
(use a comma to separate answers as needed.)
b. there are no critical points for f(x)=3x² + 5x + 1 on the domain.

Explanation:

Step1: Set derivative equal to zero

Set \( f^{\prime}(x)=0 \), so \( 6x + 5=0 \).

Step2: Solve for \( x \)

Subtract \( 5 \) from both sides: \( 6x=-5 \). Then divide by \( 6 \): \( x =-\frac{5}{6} \).

Answer:

A. The critical point(s) occur(s) at \( x =-\frac{5}{6} \)