Calculus Examples

Find the second derivative.
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Find the first derivative.
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By the Sum Rule, the derivative of with respect to is .
Evaluate .
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Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Evaluate .
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Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Since is constant with respect to , the derivative of with respect to is .
Add and .
Find the second derivative.
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By the Sum Rule, the derivative of with respect to is .
Evaluate .
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Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Since is constant with respect to , the derivative of with respect to is .
Add and .
The derivative of with respect to is .
Set the second derivative equal to then solve the equation .
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Rewrite the equation as .
Since , there are no solutions.
No solution
No solution
No values found that can make the second derivative equal to .
No Inflection Points
There are no inflection points and the interval to test the concavity on is .
The graph is concave down because the second derivative is negative.
The graph is concave down
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