Calculus 1

Activity 1.

Directions: Answer the problems below. Write the complete solution (Given, Required, Solution) of each of the problem. Thank you very much for your time and effort!

1.

Find equations of the two tangent lines to the graph of x) 2 X2 that pass through the point (1, 3). line with negative slope, if = line with positive slope, V = Find an equation of the line that is tangent to the graph of fend parallel to the given line. Function Line 1:00:32 2xy+3=} The radius r of a sphere is increasing at a rate 01'8 centimeters per minute. (a) Find the rate of change of the volume when r = 8 centimeters. (b) Find the rate of change of the volume when r = 37 centimeters. Find two positive numbers satisfying the given requirements. The product is 204 and the sum is a minimum. |:| (smaller value) (larger value} \fUse a graphing utility to verify your results. y y 12 16- 4 8- 12 4 8 X NIX 4 -4 X NIX- -4 A -8- X NIX- B -4 CX NIN -4 DAnalyze and sketch a graph of the function over the given interval. Label any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) Function Interval y = 2 (csc x + sec x) 0