Applied Problem
For my exam I was given a packet, within this packet was problems that i had to solve. It tested my ability to take what I had learned through out the year and apply it to real world applications. This packet took advance algebra, calculus and within the calculus I had to derive many equations to solve for a specific thing.
Math Skills I Used:
Find a related rate and use the related rates to solve real-life problems
Find the derivative of a composite function using the chain rule. Find the derivative of a function using the general power rule and simplify the derivatives of a function using algebra
Use the limit definition to find the derivative of a function
Find the derivative of a function using the constant rule
Find the derivative of a function using the sum and difference
Use derivatives to find rates of change
Find the derivatives of a function using the product rule
Problem 2 knowing the relation of position, acceleration, velocity and Jerk of a vehicle. I was given a graph took at and had to know what each line represented, This took intuitive skills and knowing as you decelerate you velocity decreases as well. In Problem 3 I was to find the rate of change of the height of the water. I found this by taking the derivative of the volume of a cone with volume in relation to the height. In problem 6 I had to do similar techniques with problem three but apply the chain rule and the product rule to solve for the rate of change of the area when the height is 12 ft.
Math Skills I Used:
Find a related rate and use the related rates to solve real-life problems
Find the derivative of a composite function using the chain rule. Find the derivative of a function using the general power rule and simplify the derivatives of a function using algebra
Use the limit definition to find the derivative of a function
Find the derivative of a function using the constant rule
Find the derivative of a function using the sum and difference
Use derivatives to find rates of change
Find the derivatives of a function using the product rule
Problem 2 knowing the relation of position, acceleration, velocity and Jerk of a vehicle. I was given a graph took at and had to know what each line represented, This took intuitive skills and knowing as you decelerate you velocity decreases as well. In Problem 3 I was to find the rate of change of the height of the water. I found this by taking the derivative of the volume of a cone with volume in relation to the height. In problem 6 I had to do similar techniques with problem three but apply the chain rule and the product rule to solve for the rate of change of the area when the height is 12 ft.
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Overall in this class I used basic deriving to solve for the problems. I learned that the derivative of speed is acceleration and the derivative of acceleration is called a Jerk and Jerks are a constant number. Deriving the simplest equations will show you physical aspects that you had not know two things were related. Finding the rate of change of a specific thing such as the water draining from a cone I can tell you the rate of change of that volume or height if I was given just key information. This class and these problems have allowed me to have a better understanding of the real life applications of math and especially Calculus.