INITIAL VALUE PROBLEMS EQ: HOW CAN WE FIND THE VALUE OF ‘C’ IN AN ANTI-DERIVATIVE? Particular Anti-Derivatives.

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Presentation transcript:

INITIAL VALUE PROBLEMS EQ: HOW CAN WE FIND THE VALUE OF ‘C’ IN AN ANTI-DERIVATIVE? Particular Anti-Derivatives

Example 1 Suppose f(x) represents the particular anti-derivative of 2x + 5 that satisfies the condition f(3) = 28. Find a formula for f(x).

Example 2 Find the function f(x) whose tangent has a slope of for each value of x and whose graph passes through the point (2,6)

Example 3 – Distance/Velocity/Acceleration When a hockey player strikes a puck with a certain force, the puck moves along the ice with a velocity at time t, where. Let s(t) denote the distance between the puck and the player after t seconds. Find function s(t). Initial Condition t = 0, s = 0

Example 4 – Do we always need the anti-derivative function? The acceleration of a particle moving along the x-axis at time t is given by. If the initial velocity is 10 m/s, what is the velocity after 2 seconds? Initial condition t = 0, v = 10

Example 5 – Do we always need the anti-derivative function? It is estimated that in ‘x’ months from now the population of a certain town will be changing at a rate of people per month. The current population is What will be the population 9 months from now.