The point P(7,−3) lies on the curve y= 6−x
3
. (a) If Q is the point (x, 6−x
3
), find the slope of the secant line PQ (correct to six decimal places) for the following values of x. (i) 6.9 m PQ
= (ii) 6.99 m PQ
= (iii) 6.999 m PQ
= (iv) 6.9999 m PQ
= (v) 7.1 m PQ
= (vi) 7.01 m PQ
= (vii) 7.001 m PQ
= (viii) 7.0001 m PQ
= (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(7,, - m= (c) Using the shope frem, part (b), find an equation of the tangent line to the curve at P(7,−3).