If $h(t)$ represents the height of an object above ground level at time $t$ and $h(t)$ is given by $h(t)=-16t^2+13t+1$ find the height of the object at the time when the speed is zero.
Suppose $h(t)=t^2+14t+7$ . Find the instantaneous rate of change of $h(t)$ with respect to $t$ at $t=2$ .
Suppose $G(x)=6x^2+x+4$ . Find a number $b$ such that $G'(b)=7$ .
Let $g(x)=2x^2+4x+1$ . Find a value of $c$ between 1 and 3 such that the average rate of change of $g(x)$ from $x=1$ to $x=3$ is equal to the instantaneous rate of $g(x)$ at $x=c$ .
Let $F(s)=5s^2+3s+4$ . Find a value of $d$ greater than $0$ such that the average rate of change of $F(s)$ from $0$ to $d$ equals the instantaneous rate of change of $F(s)$ at $s=1$.
Let $f(x)=x^2+x+13$. What is the value of $x$ for which the tangent line to the graph of $y=f(x)$ is parallel to the $x$-axis?
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