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Antiderivatives 4.0
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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
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Antidervative A function F is called an antiderivative of f on an interval l if F’(x) = f(x) for all x on l
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Antiderivative What function has a derivative of f(x) = 4x 2 + 3x – 7
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Antiderivative General form of the antiderivative: the general form of the antiderivative of f is F(x) + C where C is a constant
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Power Rule The antiderivative of is Add one to the exponent and divide
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Example Find the general antiderivative of
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Example Find the general antiderivative of
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Particular Solutions A particular antiderivative is an antiderivative in which we are given information to help us solve for the constant.
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Example Find f(x) if and f(0)=3
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Example Find f if and f(0)=4 and f(1)=1
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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?
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Homework Worksheet (pg 334) # 1 – 7, 13, 21, 22, 37
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