Final answer:
Projectile motion, option c, is an application of quadratic equations where the parabolic path of an object in motion is analyzed. Calculating derivatives, evaluating integrals, and solving linear equations are not typically solved using quadratic equations.
Step-by-step explanation:
Among the given options, c) Projectile motion is a scenario that can be solved using quadratic equations. A standard example of projectile motion is when an object is thrown into the air and moves along a parabolic path under the influence of gravity. The position and velocity of the object at any point in time can be predicted using quadratic equations that represent the object's horizontal and vertical motion.
Option a) Calculating derivatives and d) Evaluating integrals, fall under the domain of calculus and typically do not directly involve solving quadratic equations. Option b) Solving linear equations involves first-degree polynomials, not second-order polynomials.
To solve a projectile motion problem, we may need to find the initial velocity of a body or use a kinematic equation to solve for an unknown quantity. Given a scenario with constant acceleration (like gravity in projectile motion), one can apply appropriate kinematic equations, which often take the form of quadratic equations, to find various parameters like maximum height, range, time of flight, etc.
In conclusion, the correct option for an application scenario that can be solved using quadratic equations is c) Projectile motion.