Chapter 1.4, Problem 4E

The point P(0.5, 0) lies on the curve $y=\cos \pi x$.

(a) If Q is the point $\left(x,\cos \pi x\right)$, use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x:

(i) 0

(ii) 0.4

(iii) 0.49

(iv) 0.499

(v) 1

(vi) 0.6

(vii) 0.51

(viii) 0.501

(b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(0.5, 0).

(c) Using the slope from part(b), find an equation of the tangent line to the curve at P(0.5, 0).

(d) Sketch the curve, two of the secant lines, and the tangent line.