The point P(6, –4) lies on the curve y = 4/(5 – x). (a) If Q is the point (x, 4/(5 – x)), use your calculator to find the slope mPO of the secant line PQ (correct to six decimal places) for the following values of x. (i) 5.9 mpQ = (ii) 5.99 mpQ = (iii) 5.999 mpQ = (iv) 5.9999 mpQ = (v) 6.1 mpQ = (vi) 6.01 mPQ = (vii) 6.001 mpQ = (viii) 6.0001 mPQ = (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(6, –4). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6, -4).

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A: We will solve the problem

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A: Topic = Derivative

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A: Maximize slope

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A: as per bartleby guidelines  i can do only first question. please ask other question seperately.

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A: We can use application of derivative in order to solve the given problem.

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A: Consider the curve

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A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

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A: Follow the procedure given below.

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A: find out the slope of the curve at t=0

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A:

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A: This question is based on finding slope of parametric curve.

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Q: At what point on the curve x = 3t2 + 1, y = t3 – 5 does the tangent line have slope ? 2

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