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

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 $I$?

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.)

In the context of extrema, if all the rates of change $f^{\prime }\left(x\right)$ (derivatives) in a set of problems are negative, what does this indicate about the behavior of the functions involved?

Let the function be defined by $f\left(x\right)=x^3-3x^2+2$. At what value(s) of $x$ does $f\left(x\right)$ have a relative maximum?

A tangent line approximation of a function value is an underestimate when the function is:

Given the function $f(x,y)=x^2-y^2$, which of the following statements correctly describes its local maxima, local minima, and saddle points?