Question

for the function, find the points on the graph at which the tangent line is horizontal. if none exist, state that fact f(x)=3x^{2}-2x + 5 select the correct choice below and, if necessary, fill in the answer box within your choice. a. the point(s) at which the tangent line is horizontal is (are) (simplify your answer. type an ordered - pair. use a comma to separate answers as needed.) b. there are no points on the graph where the tangent line is horizontal c. the tangent line is horizontal at all points of the graph

Explanation:

Step1: Find the derivative

$f'(x)=\frac{d}{dx}(3x^{2}-2x + 5)=6x-2$

Step2: Set derivative equal to 0

$6x - 2=0$, then $x=\frac{1}{3}$

Step3: Find the y - value

$f(\frac{1}{3})=3(\frac{1}{3})^{2}-2(\frac{1}{3})+5=\frac{1}{3}-\frac{2}{3}+5=\frac{-1 + 15}{3}=\frac{14}{3}$

Answer:

A. $(\frac{1}{3},\frac{14}{3})$