The Tangent and Velocity Problems

Question

The point 𝑃(2,0) is on the graph of 𝑦=𝑥3−8. Let 𝑄 be the point with the coordinates(𝑥,𝑥3−8).

(a)Find a formula for the slope of the secant line 𝑃𝑄⃗⃗⃗⃗⃗ in terms of 𝑥.

(b)Find the slope of the secant line 𝑃𝑄⃗⃗⃗⃗⃗⃗ (to 3 decimal places) for the given values of 𝑥.

𝑥 1.7 1.9 1.99 2.01 2.1

Slope of secant line

(c)What number would you use as an estimate for the slope of the tangent line at𝑃(2,0)?

Answer 1

(a)

slope of the secant line is (x^3 - 8)/(x-2)

(b)

(c) 12 looks good !!!

derivative is 3x^2 which is in fact 12 when x=2