Applications of Differentiation
Applications of Differentiation 1

Critical Values:

Critical Values: Cubic  
Extreme point on a parabola  
Extrema of a cubic  

 

General Contents

Index

Home

Tangent Line:
Horizontal tangent line to a quadratic:
Horizontal tangent line to a cubic:
Horizontal tangent line to a cubic:  
Tangent line to a quadratic at a given point: at (1,4).
Tangent and Normal lines at a point on a circle:
Tangent lines to cubic with given slope: where the slope is 10
Tangent line to a rational function at a given point: tan line to at .
Tangent line to a linear plus a reciprocal at a point: tan line to at the point .
Tangent line to a fractional power at a given point: tan line to at the point .
Tangent line to a linear plus a radical at a given point: tan line to at the point .
Tangents to a parabola through a given point: For , two tan lines through .
Tangent line for a parametric curve: parabola: For what values of a and b is the line
 tangent to the parabola , when .
 
Tangent & Normal Lines via Implicit Differentiation:
Circle:
Ellipse:
Hyperbola:
Parabola:

General Contents

Index

Home

Normal Line:
Normal line to a parabola: Normal to at .
Normal line to a parabola: Normal to at .
Normal line at a point on a cubic: Point on curve where normal has slope -12.
Normal line to a parabola, its other point of intersection: Normal line to at .

Max-Min:
Minimize distance to  
Maximize area of 3 pens with a fixed length of fencing
Minimize the fencing for 4 pens with a fixed area

Minimize the sum of two numbers
Minimize the product of two numbers
Minimize the function
Maximize the product of two numbers: Example 1

Maximize the product of two numbers: Example 2
Maximize a box from a given sheet
Maximize the area under a line

Maximize the area under a parabola

Maximize the volume of a box of given Length+Girth

Maximize the strength of a beam cut from a log

Mean Value Theorem:  
Mean Value Theorem and parabola

Rolle's Theorem:  
Rolle's Theorem and cubic  
   
 

General Contents

Index

Home

Rates
Rate of a chemical reaction
Bubble
Race Car
Piston
Point moving on a Cosine Curve
Related rates: V-shaped tank:  

Business Problems
Minimize Average Cost:

Minimize Construction Cost of a Tunnel
Maximize Revenue:

Maximize Profit:
Maximize Truck Rental Profit

Differentials
Differentials: Estimate a root:
Differential: Quadratic:
Differential: radical:
Differentials: Circular field: 

Newton's Method
 Newton's Method: Quadratic:  
Newton's Method: Cubic:

General Contents

Index

Home