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Finding the Slope of Tangent Lines to a Parabola - Prof. Maria Aronne, Assignments of Calculus

Instructions and exercises on finding the slope and equation of tangent lines to a parabola at given points. It includes a graph of the function f(x) = 2x² and three tangent lines at x = -3, x = -1, and x = 2. Students are asked to find the slope and y-intercept of each tangent line and label them on the graph.

Typology: Assignments

Pre 2010

Uploaded on 09/17/2009

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Math 160 – Section 1.2 – The Slope of a curve at a Point
You have been given the graph of
2
( )y f x x
and three lines which are tangent to the
graph of
2
( )y f x x
at x = -3, -1, and 2.
a) From the graph, obtain the value of the slope and y-intercept of each of the lines. Then,
complete the table and label each of the lines on the graph.
x-
coordinate
Coordinates of the
point on the graph
Slope of line tangent
to the graph at the
given point
y-
intercept
Equation of the
tangent line
x = -3
1
y
x = -1
2
y
x = 2
3
y
1
pf2

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Math 160 – Section 1.2 – The Slope of a curve at a Point You have been given the graph of 2 yf ( ) xx and three lines which are tangent to the graph of 2 yf ( ) xx at x = -3, -1, and 2. a) From the graph, obtain the value of the slope and y-intercept of each of the lines. Then, complete the table and label each of the lines on the graph. x- coordinate Coordinates of the point on the graph Slope of line tangent to the graph at the given point y- intercept Equation of the tangent line x = -3 (^) y 1  x = -1 (^) y 2  x = 2 (^) y 3  1

b) Use the information from the previous page to complete the following table: x-coordinate of point

Slope of the tangent

  • Describe in words the pattern that lets you find the slope of the line tangent to the graph at a point in terms of the x-coordinate of the point.
  • Now describe this relationship with an expression in terms of x m = c) Use the answer to part (b) to give the value of the slope of the line tangent to 2 yf ( ) xx at the point when x = 3. Then write the equation of that line (show all work). Sketch the graph of this line on the grid from the previous page to check your answer. d) Slope of the tangent line as a rate of change The slope of the tangent line at a given point is indicating the rate at which y is changing with respect to x.
  • For the function yf ( ) xx^2 , at the point when x = 1 and y = ____ , we can say that y is increasing/decreasing at a rate of ________ units per unit.
  • For the function yf ( ) xx^2 , at the point A( _____, _____ ), y is decreasing at a rate of 6 units per unit.
  • For the function 2 yf ( ) xx , at the point B( 4, _____ ) we can say that

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