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Calculus I Review

Autor:ssvestal

A function and its derivatives

Given the graph of shown below. Graph and in the same window as the function. Then answer the questions below the graph.

Graph of the function, f(x).

The graph of the function, is increasing when the graph of the derivative, is ________________ the -axis.

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The graph of the function, is decreasing when the graph of the derivative, is ________________ the -axis.

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  • A
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  • C
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The graph of the function, is concave down when the graph of the second derivative, is ________________ the -axis.

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The graph of the function, is concave up when the graph of the second derivative, is ________________ the -axis.

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  • A
  • B
  • C
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Area under a curve

In the Geogebra window below the graph of is shown. If we want to estimate the area under the curve to the right of the -axis, we can use Riemann Sums. You will notice in the graph that we are interested in the area between and . To calculate the left-hand sum, use LeftSum(, 0, 2, n), where is the function and n is the number of rectangles.

Using the Input bar in the graph above, have Geogebra calculate the left-hand sum using 8 rectangles. Your answer is an ____________________ of the area.

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Using the Input bar in the graph above, have Geogebra calculate the LowerSum using 8 rectangles. Your answer is an ____________________ of the area.

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Now calculate the actual area using the Integral command. The actual area between the graph and the -axis is ______________ (round answer to 3 decimal places).

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Indefinite Integrals

If we want to find the general antiderivative of a function, , we use the Integral command. A function is given in the graphing window below, use Integral() to find the antiderivative.

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