Calculus Examples

,
Solve for .
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Rewrite as .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Remove parentheses.
Simplify and combine like terms.
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Simplify each term.
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Use the power rule to combine exponents.
Add and to get .
Move to the left of the expression .
Multiply by to get .
Multiply by to get .
Add and to get .
Find the derivative.
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By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
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 to get .
Since is constant with respect to , the derivative of with respect to is .
Add and to get .
Evaluate the derivative at , which is the slope of the tangent line at .
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Multiply by to get .
Add and to get .
Use the point-slope formula , where and are the values of the point and is the slope of the tangent line.
Simplify.
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The slope-intercept form is , where is the slope and is the y-intercept.
Rewrite in slope-intercept form.
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Simplify the right side.
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Multiply by to get .
Apply the distributive property.
Multiply by to get .
Move all terms not containing to the right side of the equation.
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Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.
Subtract from to get .
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