Calculus Examples

Find the Horizontal Tangent Line y=x^2+5
Step 1
Set as a function of .
Step 2
Find the derivative.
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Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Since is constant with respect to , the derivative of with respect to is .
Step 2.4
Add and .
Step 3
Divide each term in by and simplify.
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Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Cancel the common factor of .
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Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Divide by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Divide by .
Step 4
Solve the original function at .
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Step 4.1
Replace the variable with in the expression.
Step 4.2
Simplify the result.
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Step 4.2.1
Raising to any positive power yields .
Step 4.2.2
Add and .
Step 4.2.3
The final answer is .
Step 5
The horizontal tangent line on function is .
Step 6
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