find a) any critical values and b) any relative extrema. t(x)=x³ + 13x - 1 a) select the correct choice…

find a) any critical values and b) any relative extrema. t(x)=x³ + 13x - 1 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 + 13x - 1 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 of the function

The derivative of (t(x)=x^{3}+13x - 1) using the power rule ((x^{n})^\prime=nx^{n - 1}) is (t^\prime(x)=3x^{2}+13).

Step2: Set the derivative equal to zero and solve for (x)

Set (t^\prime(x)=0), so (3x^{2}+13 = 0). Then (3x^{2}=-13), and (x^{2}=-\frac{13}{3}). Since the square of a real - number (x) (i.e., (x^{2})) is non - negative for all real (x) ((x^{2}\geq0) for (x\in R)), there are no real solutions for (x) from the equation (x^{2}=-\frac{13}{3}).

Answer:

B. The function has no critical values.