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:- A curve has equation y = f(x)

Write an expression for the slope of the secant line through the points

P(3,f(3)) and Q(x,f(x))

Write an expression for the slope of the tangent line at P.

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Reid Wolff
Reid WolffLv2
27 May 2020

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Related questions

The point lies on the curve .

  1. If Q is the point , use your calculator to find the slope of the secant line PQ ( correct to six decimal places) for the following values.

    1. 0

    2. 0.4

    3. 0.49

    4. 0.499

    5. 1

    6. 0.6

    7. 0.51

    8. 0.501

  2. Using the results of part (a), guess the value of the slope of the tangent line to the curve at

  3. Using the slope from part (b), find an equation of the tangent line to the curve at .

  4. Sketch the curve, two of the secant lines, and the tangent line.

Write an expression for the slope of the tangent line to the curve at the point.

The slope of the line tangent to the curve y = f (x) at the point P (a, f(a)) is given by mtan = lim- x+a f (x) - f (a) -, if the limit exists. X - a 5. (12 pts) Let £ (x) and a = 5. (a) Using the definition above, find the slope, mtan of the line tangent to the graph off at P (a, f (a)). (b) Find an equation of the tangent line in part (a).

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