find a) any critical values and b) any relative extrema. t(x)=x³ + 6x + 6 a) select the correct choice below…

find a) any critical values and b) any relative extrema. t(x)=x³ + 6x + 6 a) select the correct choice below and, if necessary, fill in the answer box within your choice. a. the critical value(s) of the function is/are (use a comma to separate answers as needed.) b. the function has no critical values.

find a) any critical values and b) any relative extrema. t(x)=x³ + 6x + 6 a) select the correct choice below and, if necessary, fill in the answer box within your choice. a. the critical value(s) of the function is/are (use a comma to separate answers as needed.) b. the function has no critical values.

Answer

Explanation:

Step1: Find the derivative

Differentiate $t(x)=x^{3}+6x + 6$ using the power - rule. The derivative $t'(x)=3x^{2}+6$.

Step2: Set the derivative equal to zero

Set $t'(x) = 0$, so $3x^{2}+6=0$. Then $3x^{2}=-6$, and $x^{2}=- 2$. Since there is no real number $x$ such that $x^{2}=-2$, there are no critical values.

Answer:

B. The function has no critical values.