Tangent Lines 1.Equation of lines 2.Equation of secant lines 3.Equation of tangent lines.

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Presentation transcript:

Tangent Lines 1.Equation of lines 2.Equation of secant lines 3.Equation of tangent lines

Equation of Lines Write the equation of a line that passes through (-3, 1) with a slope of – ½. or

Equation of Lines Write the equation of a line that passes through (0, 1) with a slope of ½. or

Equation of Lines Write the equation of the line. or

Lines When writing the equation of a line that passes through (0, 1) with a slope of -3. What is the missing blue number? A -3 B -1 C 0 D 1

Lines When writing the equation of a line that passes through (0, 1) with a slope of -3. What is the missing blue number? A -3 B -1 C 0 D 1

Passes through (0, 1) with a slope of -3. The missing blue number was zero

Write the equation of a green line that passes through (0, 1) with a slope of -3. What is the missing green number m? A -3 B -1 C 0 D 1

Write the equation of a green line that passes through (0, 1) with a slope of -3. What is the missing green number m? A -3 B -1 C 0 D 1

Secant Lines Write the equation of the secant line that passes through and (200, 220).

What is the slope of this secant line that passes through (200, 220) and (184, 210) ?

A 5/9 B 5/7 C 5/8 D 10/6 E 10/12

What is the slope of this secant line that passes through (200, 220) and (184, 210) ? A 5/9 B 5/7 C 5/8 D 10/6 E 10/12

Secant Lines Write the equation of the secant line that passes through and (200, 220).

/java/p6.html Secant Lineshttp://math.georgiasouthern.edu/~bmclean /java/p6.html pjymE Derivehttp:// pjymE

pjymE Derivehttp:// pjymE

The slope of f(x) =x 2 and when x = 1

Find the slope of the tangent line of f(x) = x 2 when x = x. 1. Calculate f(x+h) – f(x) f(x+h) = x 2 + 2xh + h 2 f(x) = x 2 f(x+h) – f(x) = 2xh + h Divide by h and get 2x + h 3. Let h go to 0

Find the slope of f(x)=x 2 A.2x+h B.2x C.x 2

Find the slope of f(x)=x 2 A.2x+h B.2x C.x 2

Find the slope of the tangent line of f(x) = x 2 when x = x. 1. Calculate f(x+h) – f(x) f(x+h) = x 2 + 2xh + h 2 f(x) = x 2 f(x+h) – f(x) = 2xh + h Divide by h and get 2x + h 3. Let h go to 0 and get 2x

Finding the slope of the tangent line of f(x) = x 2, f(x+h) - f(x) = A.(x+h) 2 – x 2 B.x 2 + h 2 – x 2 C.(x+h)(x – h)

Finding the slope of the tangent line of f(x) = x 2, f(x+h) - f(x) = A.(x+h) 2 – x 2 B.x 2 + h 2 – x 2 C.(x+h)(x – h)

(x+h) 2 – x 2 = A. x 2 + 2xh + h 2 B.h 2 C.2xh + h 2

(x+h) 2 – x 2 = A. x 2 + 2xh + h 2 B.h 2 C.2xh + h 2

= A. 2x B.2x + h 2 C.2xh

= A. 2x B.2x + h 2 C.2xh

Find the slope of the tangent line of f(x) = 2x + 3 when x = x. 1. Calculate f(x+h) – f(x) f(x+h) = 2(x+h) + 3 f(x) = 2x + 3 f(x+h) = 2x + 2h + 3 f(x) = 2x +3 f(x+h)-f(x) = 2h 2. Divide by h and get 2 3. Let h go to 0 and get 2

= 0 Rule 5

sin(0.0018) = A 1.8 B 0.18 C D E

sin(0.0018) = A 1.8 B 0.18 C D E

Rule 4

= 0 Rule 5

. A 12 B 6 C 1 D 0 E -1

. A 12 B 6 C 1 D 0 E -1

.

. 1 * 0

. A 12 B 6 C 1 D 0 E -1

. A 12 B 6 C 1 D 0 E -1

.

.

.

.

.

. A 0 B ½ C 1 D 4 E 8

. A 0 B ½ C 1 D 4 E 8

Write the equation of the line tangent to y = x + sin(x) when x = 0 given the slope there is 2. A.y = 2x + 1 B.y = 2x C.y = 2x

Write the equation of the line tangent to y = x + sin(x) when x = 0 given the slope there is 2. A.y = 2x + 1 B.y = 2x C.y = 2x