The point

P(5,3)

lies on the curve

y=3/(4x).

(a) IfQis the point

(x,3/(4x)),

use your calculator to find the slope

m_PQ

of the secant linePQ(correct to six decimal places) for the following values ofx.(i) 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=

(viii) 5.0001

m_PQ=

(b) Using the results of part (a), guess the value of the slopemof the tangent line to the curve at

P(5,3).

m=

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

P(5,3).

y=3x18