Calculus Examples

Find the Inflection Points f(x)=1/x
Step 1
Find the second derivative.
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Step 1.1
Find the first derivative.
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Step 1.1.1
Rewrite as .
Step 1.1.2
Differentiate using the Power Rule which states that is where .
Step 1.1.3
Rewrite the expression using the negative exponent rule .
Step 1.2
Find the second derivative.
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Step 1.2.1
Differentiate using the Product Rule which states that is where and .
Step 1.2.2
Differentiate.
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Step 1.2.2.1
Rewrite as .
Step 1.2.2.2
Multiply the exponents in .
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Step 1.2.2.2.1
Apply the power rule and multiply exponents, .
Step 1.2.2.2.2
Multiply by .
Step 1.2.2.3
Differentiate using the Power Rule which states that is where .
Step 1.2.2.4
Multiply by .
Step 1.2.2.5
Since is constant with respect to , the derivative of with respect to is .
Step 1.2.2.6
Simplify the expression.
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Step 1.2.2.6.1
Multiply by .
Step 1.2.2.6.2
Add and .
Step 1.2.3
Simplify.
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Step 1.2.3.1
Rewrite the expression using the negative exponent rule .
Step 1.2.3.2
Combine and .
Step 1.3
The second derivative of with respect to is .
Step 2
Set the second derivative equal to then solve the equation .
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Step 2.1
Set the second derivative equal to .
Step 2.2
Set the numerator equal to zero.
Step 2.3
Since , there are no solutions.
No solution
No solution
Step 3
No values found that can make the second derivative equal to .
No Inflection Points