a. find the open intervals on which the function is increasing and those on which it is decreasing b…

a. find the open intervals on which the function is increasing and those on which it is decreasing b. identify the functions local extreme values, if any, saying where they occur. f(t)=3t^3 + 14t a. on what open interval(s), if any, is the function increasing? select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the function f is increasing on the open interval(s) (type your answer in interval notation. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.) b. the function is never increasing. on what open interval(s), if any, is the function decreasing? select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the function f is decreasing on the open interval(s) (type your answer in interval notation. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.) b. the function is never decreasing. b. find each local maximum, if any. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (type integers or simplified fractions.) a. the function has a local maximum value at two values of t in increasing order of t - value, the maximum values are f( ) = and f( ) =

a. find the open intervals on which the function is increasing and those on which it is decreasing b. identify the functions local extreme values, if any, saying where they occur. f(t)=3t^3 + 14t a. on what open interval(s), if any, is the function increasing? select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the function f is increasing on the open interval(s) (type your answer in interval notation. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.) b. the function is never increasing. on what open interval(s), if any, is the function decreasing? select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the function f is decreasing on the open interval(s) (type your answer in interval notation. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.) b. the function is never decreasing. b. find each local maximum, if any. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (type integers or simplified fractions.) a. the function has a local maximum value at two values of t in increasing order of t - value, the maximum values are f( ) = and f( ) =

Answer

Explanation:

Step1: Find the derivative

The derivative of $f(t)=3t^{3}+14t$ using the power - rule $(x^n)^\prime=nx^{n - 1}$ is $f^\prime(t)=9t^{2}+14$.

Step2: Analyze the sign of the derivative

Since $t^{2}\geq0$ for all real $t$, then $9t^{2}\geq0$. So $f^\prime(t)=9t^{2}+14\geq14>0$ for all real $t$.

Answer:

a.

  • The function $f$ is increasing on the open interval $(-\infty,\infty)$.
  • The function is never decreasing. b. The function has no local maximum or minimum values. So the answer for part b is: The function has no local maximum values.