If Q is the point (x, 4/(4 - x), use your calculator to find the slope m_PQ of t

Question

If Q is the point (x, 4/(4 - x), use your calculator to find the slope m_PQ of the secant line PQ (correct to six decimal places) for the following values. (i0 4.9 m_PQ = (ii) 4.99 m_PQ = (iii) 4.999 m_PQ = (iv) 4.9999 m_PQ = (v) 5.1 m_PQ = (vi) 5.01 m_PQ = (vii) 5.001 m_PQ = (viii0 5.0001 m_PQ = (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P (5, -4) m = (c)Using the slope from part (b), find an equation of the tangent line to the curve at P(5, -4).

Explanation / Answer

here slope of any point on curve y

is dy/dx =4/(4-x)2

therefore

b) from above the value at x=5 ; is mpq =4

c)as equation of line : y-y1 =mpq(x-x1)

hence y-(-4) =4(x-5)

y+4 =4x-20

y=4x-24

x mpq 4.9 4.938272 4.99 4.081216 4.999 4.008012 4.9999 4.000800 5.1 3.305785 5.01 3.921184 5.001 3.992012 5.0001 3.999200

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