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

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.

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?

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 $f\left(x\right)$?

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

Consider the graph of $f^{\prime }\left(x\right)$ below. How many local maxima does $f\left(x\right)$ have?

Given the function $f\left(t\right)=t^3-3t^2+2$, for which values of $t$ is the curve concave upward? (Select the correct interval.)

For the curve $y=7\ln \left(x\right)$, at what value of $x$ does the curve have maximum curvature?