The position function of a particle is given by $s\left(t\right)=t^3-6t^2+9t+2$. At what time $t$ is the speed of the particle minimum?

Finding Extrema from Graphs

In Exercises 11–14, match the table with a graph.

Finding Extreme Values

In Exercises 1–10, find the extreme values (absolute and local) of the function over its natural domain, and where they occur.

y = 𝓍³ ― 2𝓍 + 4

Finding Extreme Values

In Exercises 1–10, find the extreme values (absolute and local) of the function over its natural domain, and where they occur.

y = 𝓍³ + 𝓍² ― 8𝓍 + 5

101. In Exercises 101 and 102, the graph of f' is given. Determine x-values corresponding to local minima, local maxima, and inflection points for the graph of f.

Which of the following could be a turning point for the continuous function $f\left(x\right)$?

Which of the following is a possible turning point for the continuous function $f\left(x\right)$?

For the function $f\left(x\right)=-x^2+4x+1$, at which $x$-value does a local maximum occur?

Which of the following best describes the difference between a relative maximum and an absolute maximum of a function on an interval $I$?