9/2/1 You learned in previous courses that the slope of a non-vertical straight line is or...

 

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Δεν 9/2/1 You learned in previous courses that the slope of a non-vertical straight line is or Ar 22 21 where (1.1) and (22, y2) are any two points on the line. Most functions we see in calculus have the property that if we pick a point on the graph of the function and zoom in, we will see a straight line. 1. Graph the function f(x) = x³- 6x + 3 for -3 << 4. Zoom in on the point (1,-2) (notice that f(1) = -2 for the y-coordinate). Keep zooming in on that point until the graph looks like a straight line. Fill in the "coordinates" of the window for this view in the form [2 min, max] x [y min, y max]: Zoomed window: Using the TRACE mode on your calculator, pick another point on the curve in this window other than (1,-2). Calculate the slope of the straight line through these two points: Other point: ; Slope The number for the slope above is an approximation to the slope of the function f(x) = 23-6x+3 at the point (1,-2). This slope is also called the derivative of f at x = 1, and is denoted by f' (1). Now, for the same function, zoom in on the point (-3, -6) and do the same thing; that is, find f'(-3): Δεν 9/2/1 You learned in previous courses that the slope of a non-vertical straight line is or Ar 22 21 where (1.1) and (22, y2) are any two points on the line. Most functions we see in calculus have the property that if we pick a point on the graph of the function and zoom in, we will see a straight line. 1. Graph the function f(x) = x³- 6x + 3 for -3 << 4. Zoom in on the point (1,-2) (notice that f(1) = -2 for the y-coordinate). Keep zooming in on that point until the graph looks like a straight line. Fill in the "coordinates" of the window for this view in the form [2 min, max] x [y min, y max]: Zoomed window: Using the TRACE mode on your calculator, pick another point on the curve in this window other than (1,-2). Calculate the slope of the straight line through these two points: Other point: ; Slope The number for the slope above is an approximation to the slope of the function f(x) = 23-6x+3 at the point (1,-2). This slope is also called the derivative of f at x = 1, and is denoted by f' (1). Now, for the same function, zoom in on the point (-3, -6) and do the same thing; that is, find f'(-3): Δεν 9/2/1 You learned in previous courses that the slope of a non-vertical straight line is or Ar 22 21 where (1.1) and (22, y2) are any two points on the line. Most functions we see in calculus have the property that if we pick a point on the graph of the function and zoom in, we will see a straight line. 1. Graph the function f(x) = x³- 6x + 3 for -3 << 4. Zoom in on the point (1,-2) (notice that f(1) = -2 for the y-coordinate). Keep zooming in on that point until the graph looks like a straight line. Fill in the "coordinates" of the window for this view in the form [2 min, max] x [y min, y max]: Zoomed window: Using the TRACE mode on your calculator, pick another point on the curve in this window other than (1,-2). Calculate the slope of the straight line through these two points: Other point: ; Slope The number for the slope above is an approximation to the slope of the function f(x) = 23-6x+3 at the point (1,-2). This slope is also called the derivative of f at x = 1, and is denoted by f' (1). Now, for the same function, zoom in on the point (-3, -6) and do the same thing; that is, find f'(-3):

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To graph the function fx x3 6x 3 for 3 leq x leq 4 and zoom in on the point 1 2 we can follow these ... View the full answer