91Ó°ÊÓ

Graph each function and then find the specified limits. When necessary, state that the limit does not exist. $$ g(x)=|x|+1 ; \text { find } \lim _{x \rightarrow-3} g(x) \text { and } \lim _{x \rightarrow 0} g(x). $$

For each function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact. $$ y=x^{2}-3 $$

For each function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact. $$ y=-x^{3}+1 $$

For each function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact. $$ f(x)=\frac{1}{3} x^{3}-3 x^{2}+9 x-9 $$

For each function, find the points on the graph at which the tangent line has slope 1 . $$ y=-0.025 x^{2}+4 x $$

The view \(V,\) or distance in miles, that one can see to the horizon from a height \(h,\) in feet, is given by $$ V=1.22 \sqrt{h} $$. a) Find the rate of change of \(V\) with respect to \(h\). b) How far can one see to the horizon from an airplane window at a height of \(40,000 \mathrm{ft} ?\) c) Find the rate of change at \(h=40,000\). d) Explain the meaning of your answer to part (c).

Find the interval(s) for which \(f^{\prime}(x)\) is positive. Find the points on the graph of $$ y=2 x^{6}-x^{4}-2 $$ at which the tangent line is horizontal.