Calculus I
Lab 07
Directions
Go to https://student.desmos.com/ and enter the code 5MUPQA. Your work saves automatically. You may use your book and notes, and this lab may require some scratch work. Complete the following (there are corresponding slides for each problem):
Problem 0
Enter in your name, I need to know who to give the grades to.
Problem 1
A police car (blue) traveling south towards Nacogdoches at 160 km/h pursues a truck (red) traveling east away from Nacogdoches at 140 km/h. At time \(t=0\), the police car is 20 km north and the truck is 30 km east of Nacogdoches.
- Find a formula for the distance between the two cars and enter this into Desmos.
- Use Desmos to calculate the rate at which the distance between the
vehicles is changing at time:
- \(t=0\);
- \(t=5\) minutes.
Problem 2
Let \(h(x) = x^2-8\ln x\). Graph \(h\) on \([1,4]\) and find the absolute maximum and absolute minimum of \(h\) on this closed interval.
Problem 3
An unknown function \(f(x)\) which is continuous on \([-2,3]\) has derivative \(g(x)\), whose graph is given to you. Do not graph f(x) (you may evaluate \(f\) at points, for example you may enter \(f(-2)\) into Desmos to see the value of \(f\) at -2). Find the absolute maximum and minimum of \(f\) on \([-2,3]\).