Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
Last call for the "Gradient Function" Investigation...
Goals:
­ Calculate the gradient of a curve at a given point
What is a gradient function?
What is differentiation?
­ Find the equation of the tangent and the normal to a curve
Vocabulary:
Gradient of a curve
Tangent
Normal
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Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
HW Quiz #6.2
1. Find , for the following function.
2. Find , for the following function.
3. What is a gradient function? 2
Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
http://www.geogebra.org/m/2984993
Goals:
1. Find the gradient function.
2. What is the gradient of the curve at x = 1? At x = 0?
3. When does ?
­ Calculate the gradient of a curve at a given point
5. Find the equation of the line passing through the two points in #4.
­ Find the equation of the tangent and the normal to a curve
6. Find the equation of the line tangent to the curve at x = ­1.
Vocabulary:
7. Find the equation of the line normal to the curve at x = ­1. Gradient of a curve
4. At what two points on the curve is the gradient of the curve equal to 7?
Tangent
Normal
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Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
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Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
1. Find the gradient function.
2. What is the gradient of the curve at x = 1? At x = 0?
3. When does ?
4. At what two points on the curve is the gradient of the curve equal to 7?
5. Find the equation of the line passing through the two points in #4.
6. Find the equation of the line tangent to the curve at x = ­1.
7. Find the equation of the line normal to the curve at x = ­1. 5
Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
1. Find the gradient function.
2. What is the gradient of the curve at x = 1? At x = 0?
3. When does ?
4. At what two points on the curve is the gradient of the curve equal to 7?
5. Find the equation of the line passing through the two points in #4.
6. Find the equation of the line tangent to the curve at x = ­1.
7. Find the equation of the line normal to the curve at x = ­1. 6
Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
Try this, individually:
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Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
Example:
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Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
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Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
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Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
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Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
Example: 1) Find the equation of the tangent and 2) Find the equation of the normal at the point (­1, 5) for http://www.geogebra.org/m/2987257
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Math Studies 6.3­6.4 Slope of Tangent + Eq. of Tangent and Normal
March 25, 2016
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