Antiderivatives 4.0. objectives  define an antiderivative  determine a general antiderivative of a function  determine a particular antiderivative.

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Presentation transcript:

Antiderivatives 4.0

objectives  define an antiderivative  determine a general antiderivative of a function  determine a particular antiderivative of a function  find a position function given initial velocity and position

Antidervative  A function F is called an antiderivative of f on an interval l if F’(x) = f(x) for all x on l

Antiderivative What function has a derivative of f(x) = 4x 2 + 3x – 7

Antiderivative  General form of the antiderivative: the general form of the antiderivative of f is F(x) + C where C is a constant

Power Rule  The antiderivative of is  Add one to the exponent and divide

Example  Find the general antiderivative of

Example  Find the general antiderivative of

Particular Solutions  A particular antiderivative is an antiderivative in which we are given information to help us solve for the constant.

Example  Find f(x) if and f(0)=3

Example  Find f if and f(0)=4 and f(1)=1

Put the antiderivative to work  Ethan is standing on top of a platform 90 feet above the ground and throws a ball straight up at a speed of 64 ft/sec. How high is the ball three seconds after the ball is thrown?

Homework  Worksheet (pg 334) # 1 – 7, 13, 21, 22, 37