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Magazine Problem 19
Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=-2 x^{3}-2 \sqrt{x+2} \text { at } x=\frac{1}{4}$$
Problem 20
Make a complete graph of each function. Locate all features of interest. $$y=x^{2}-3 x+2$$
Problem 20
Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=\sqrt{x^{2}+3 x} \text { at } x=2$$
Problem 21
Make a complete graph of each function. Locate all features of interest. $$y=x^{3}+4 x^{2}-5$$
Problem 21
Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=2 x+x^{2} \text { at } x=1$$
Problem 22
Make a complete graph of each function. Locate all features of interest. $$y=x^{4}-x^{2}$$
Problem 22
Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=x^{3}-x \text { at } x=2$$
Problem 23
Graph the region bounded by the given curves. \(y=3 x^{2}\) and \(y=2 x\)
Problem 23
Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=x+x^{3} \text { at } x=-1$$
Problem 24
Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=x^{4}+x \text { at } x=1$$
