find the critical points of the following function. f(x)=5x² + 3x + 1 select the correct choice below and…

find the critical points of the following function. f(x)=5x² + 3x + 1 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.

find the critical points of the following function. f(x)=5x² + 3x + 1 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.

Answer

Explanation:

Step1: Find the derivative

The derivative of $f(x)=5x^{2}+3x + 1$ using the power - rule $(x^n)'=nx^{n - 1}$ is $f'(x)=10x+3$.

Step2: Set the derivative equal to zero

Set $f'(x)=0$, so $10x + 3=0$.

Step3: Solve for x

Subtract 3 from both sides: $10x=-3$. Then divide by 10: $x=-\frac{3}{10}$.

Answer:

A. The critical point(s) occur(s) at $x =-\frac{3}{10}$