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STUDENT SCREEN PREVIEW F Folding the net to form a box. Enter a lenght, width, size of square to cut out. length width rotate vertically + rotate side to side cut < 2 of 7 Next >
STUDENT SCREEN PREVIEW How can Calculus be applied? L = 10.5 The paper dimmensions are 5.8 in X 10.5 in. 3 The volume of the box is 7.06 in H a=2.1 23 W = 5.8 Use the sketch tools to label how calculus can be applied. box volume 10 7.06 0 ✓ T √ 55 IC X 3 2.1 inches.gth of square < 3 of 7 Next >
STUDENT SCREEN PREVIEW Suppose we were able to cut out six identical squares from a sheet of paper the size of Colorado and form a box. ? length ? 280-miles! x miles Is Colorado the most rectangular state? The dimensions of Colorado is about 280 miles by 380 miles. mater ? length ? P Due tapa Wabrdn SARK UN F miles 380 miles Create a formula where x represents the side length of the square and V(x) represents the volume of the box. Write your volume as the product of the dimensions of the box. V(x) = 000 Submit and Explain < 4 of 7 Next >
STUDENT SCREEN PREVIEW 1000000 800000 1) Use the sketch tools to identify, if any, critical points, inflection points and global/local max/min. 600000 -400000 200000 0 cubic miles T V(x) = ✓ = 8 ((280 – 3x)) (380 – 2x) (x) = 3r³ – 850x² + 53 200x (39.53, 960079.448) 50 2 (93.3,0) 100 X miles 2) First interpret the description based on if the first and second derivative is positive/negative. 3) Fill in the table with the correct open intervals. Write, DNE, if the interval does not exist. Description increasing at an decreasing rate increasing at an increasing rate decreasing at an increasing rate decreasing at an decreasing rate critical point(s): inflection point(s): Global max point(s): Global min point(s): Local max point(s): Local min point(s) V', V" +/- open interval Submit 5 of 7 Next >
STUDENT SCREEN PREVIEW miles L = 280- The dimensions of Colorado is about 280 miles by 380 miles. L We Uge Depen miles W = 380 The formula for the volume of the box for a given side length x was V(x) = 3x³ - 850x² +53 200x 1) Calculate d à (V(x)) = (3x³ – 850x² + 53 200x) d dt dV 2) Explain the meaning of and dt 3) If the side length increases at 30 miles per hour, then what is the instantaneous rate of the volume when the side length is 75 miles. 1) 2) 3) dx dt √ Share With Class < 6 of 7 Next >