Chapter 24

Make a complete graph of each function. Locate all features of interest. $$y=4 x^{2}-5$$

write the equations of the tangent and normal at the given point. Check some by calculator. $$y=x^{2}+2 \quad \text { at } x=1$$

Use the derivative to say whether each function is increasing or decreasing at the value indicated. Check by graphing. $$y=3 x^{2}-4 \text { at } x=2$$

Make a complete graph of each function. Locate all features of interest. $$y=3 x-2 x^{2}$$

write the equations of the tangent and normal at the given point. Check some by calculator. $$y=x^{3}-3 x \quad \text { at }(2,2)$$

Make a complete graph of each function. Locate all features of interest. $$y=5-\frac{1}{x}$$

write the equations of the tangent and normal at the given point. Check some by calculator. $$y=3 x^{2}-1 \quad \text { at } x=2$$

Use the derivative to say whether each function is increasing or decreasing at the value indicated. Check by graphing. $$y=4 x^{2}-x \text { at } x=-2$$

Make a complete graph of each function. Locate all features of interest. $$y=\frac{3}{x}+x^{2}$$

write the equations of the tangent and normal at the given point. Check some by calculator. $$y=x^{2}-4 x+5 \text { at }(1,2)$$

Use the derivative to say whether each function is increasing or decreasing at the value indicated. Check by graphing. $$y=x^{3}+2 x-4 \text { at } x=-1$$

Make a complete graph of each function. Locate all features of interest. $$y=x^{4}-8 x^{2}$$

write the equations of the tangent and normal at the given point. Check some by calculator. $$x^{2}+y^{2}=25 \quad \text { at }(3,4)$$

Make a complete graph of each function. Locate all features of interest. $$y=\frac{1}{x^{2}-1}$$

Use the derivative to say whether each function is increasing or decreasing at the value indicated. Check by graphing. $$y=x^{3}-4 x \text { at } x=2$$

Make a complete graph of each function. Locate all features of interest. $$y=x^{3}-9 x^{2}+24 x-7$$

Find the first quadrant point on the curve \(y=x^{3}-3 x^{2}\) at which the slope \(=9\).

Use the derivative to say whether each function is increasing or decreasing at the value indicated. Check by graphing. $$y=x^{3}+x^{2} \text { at } x=-2$$

Make a complete graph of each function. Locate all features of interest. $$y=x \sqrt{1-x}$$

Use the derivative to say whether each function is increasing or decreasing at the value indicated. Check by graphing. $$y=x^{4}+x-3 \text { at } x=0$$

Make a complete graph of each function. Locate all features of interest. $$y=5 x-x^{5}$$

Use the derivative to find the values of \(x\) for which each function is increasing, and for which it is decreasing. Check by graphing. $$y=3 x+5$$

Make a complete graph of each function. Locate all features of interest. $$y=\frac{9}{x^{2}+9}$$

Use the derivative to find the values of \(x\) for which each function is increasing, and for which it is decreasing. Check by graphing. $$y=4 x^{2}+16 x-7$$

Make a complete graph of each function. Locate all features of interest. $$y=\frac{6 x}{3+x^{2}}$$

Find the angle(s) of intersection, to nearest tenth of a degree, between the given curves. $$y=2-x \text { and } y=x^{2} \quad \text { at }(1,1)$$

Find the angle(s) of intersection, to nearest tenth of a degree, between the given curves. $$y=2 x \text { and } y=2-x^{2} \quad \text { at }(0.732,1.46)$$

Use the derivative to find the values of \(x\) for which each function is increasing, and for which it is decreasing. Check by graphing. $$y=2 x^{3}+4 x$$

Make a complete graph of each function. Locate all features of interest. $$y=x^{3}-6 x^{2}+9 x+3$$

Find the angle(s) of intersection, to nearest tenth of a degree, between the given curves. $$y=x^{2}+x-2 \text { and } y=x^{2}-5 x+4 \text { at }(1,0)$$

Make a complete graph of each function. Locate all features of interest. $$y=x^{2} \sqrt{6-x^{2}}$$

Find the angle(s) of intersection, to nearest tenth of a degree, between the given curves. $$y=-2 x \text { and } y=x^{2}(1-x) \text { at }(0,0),(2,-4), \text { and }(-1,2)$$

Make a complete graph of each function. Locate all features of interest. $$y=\frac{96 x-288}{x^{2}+2 x+1}$$

Use the derivative to find the values of \(x\) for which each function is increasing, and for which it is decreasing. Check by graphing. $$y=5 x+x^{5}$$

Make a complete graph of each function. Locate all features of interest. $$y=\frac{\sqrt{x}}{x-1}$$

Make a complete graph of each function. Locate all features of interest. $$y=\frac{x}{\sqrt{x^{2}+1}}$$

Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=x^{4}+x^{2} \text { at } x=2$$

Make a complete graph of each function. Locate all features of interest. $$y=\frac{x^{3}}{\left(1+x^{2}\right)^{2}}$$

Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=4 x^{5}-5 x^{4} \text { at } x=1$$

Make a complete graph of each function. Locate all features of interest. $$y=x^{2}+2 x$$

Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=-2 x^{3}-2 \sqrt{x+2} \text { at } x=\frac{1}{4}$$

Make a complete graph of each function. Locate all features of interest. $$y=x^{2}-3 x+2$$

Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=\sqrt{x^{2}+3 x} \text { at } x=2$$

Make a complete graph of each function. Locate all features of interest. $$y=x^{3}+4 x^{2}-5$$

Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=2 x+x^{2} \text { at } x=1$$

Make a complete graph of each function. Locate all features of interest. $$y=x^{4}-x^{2}$$

Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=x^{3}-x \text { at } x=2$$

Graph the region bounded by the given curves. \(y=3 x^{2}\) and \(y=2 x\)

Use the second derivative to state whether each curve is concave upward or concave downward at the given value of \(x .\) Check by graphing. $$y=x+x^{3} \text { at } x=-1$$

Graph the region bounded by the given curves. \(y^{2}=4 x, x=5,\) and the \(x\) axis, in the first quadrant