The pointP(4,4)

lies on the curvey=4/3x

.

(a)

IfQis the point(x,4/3x)

,

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

(i)

3.9

m_PQ=

(ii)

3.99

m_PQ=

(iii)

3.999

m_PQ=

(iv)

3.9999

m_PQ=

(v)

4.1

m_PQ=

(vi)

4.01

m_PQ=

(vii)

4.001

m_PQ=

(viii)

4.0001

m_PQ=

(b)

Using the results of part (a), guess the value of the slope of the tangent line to the curve atP(4,4).

m=

(c)

Using the slope from part (b), find an equation of the tangent line to the curve atP(4,4).