Calculus AB Assignment Determining Slope Note: You may NOT use your calculator to calculate derivatives explicitly (for example, with the nDeriv command or through the graphing calculate menu). If you need to find a derivative, you must evaluate the derivative algebraically, then you may use your calculator to evaluate this expression, if necessary. 1. Find the slope of the tangent line to the curvey : x3 2x2 +1 at the point 1,0 . Find the equation of that tangent line. On your calculator, graph both the curve and the tangent line on the same set of axes with viewing windOWx : 2,3 , y : [2,2 . [Show all work, except for anything concerning the graphs you made on your calculatorthey were for your observation only.] 2. Find the slope of the tangent line to the curvey : 13': at the point (%,1). Find the equation of that tangent line. On your calculator, graph both the curve and the tangent line on the same set of axes with viewing windOWx : [1,1 , y : [2,2 . [Show all work, except for anything concerning the graphs you made on your calculatorthey were for your observation only.] 10 cosx : si1:ua:+l+.2x2 3. Be|0w is a graph of the curve y = Find the slopes of the tangent lines to the curve at x = 5, x = 0 and x = 5. 4. Here is a graph of the curvey = x5 5x3 +4x: 10 'I ' -m Your friend tells you that the slope of the tangent line to the curve at x = 1 is the same as the slope of the tangent line to the curve at x = 1. Prove mathematically whether your friend is right or wrong. Is the slope of the tangent line to the curve at x = a the same as the slope of the tangent line to the curve at x = a for any other values of a? Explain. t 5. Below is a graph of the curvey = 4x 3 cosx: 10 Ax /\\ a \\ \\ //\\\\ 5 / \\ f \\ f \\ 'i i \\ (\\ f \\ \" l, \\i \\ l' l A ' ~ L. . 10 i *5 0 \\ is i 10 \\ fl \\J} \\ ff X ".' if \\\\ if K'- ' i' '1. \\\\ f .5 \\/ i\" 'x/ \\ V 710 Your friend claims that the slope of the tangent line to the curve at x = 4 is the negative ofthe slope of the tangent line to the curve at x = 74. Prove mathematically whether your friend is right or wrong. Is the slope of the tangent line to the curve at x = a the negative of the slope of the tangent line to the curve at x = 7a for any other values of a? Explain. Calculus AB Assignment Determining Slope 6. Below is a graph of the curvey = m: (x2+3) 10 -10 Looking at the graph, it's clear that the function has three zeros in the domain 75 s x E 5. Find the three zeros, and find the slopes of the tangent lines to the curve at those x values