(a) The tangent line to the curve y = x at the point A(1, 1) intersects the...

(a) The tangent line to the curve y = x³ at the point A(1, 1) intersects the curve at another point B. Let R be the area of the region bounded by the curve and the tangent line. The tangent line at B intersects the curve at another point C (see figure). Let S be the area of the region bounded by the curve and this second tangent line. How are the areas R and S related?

(b) Repeat the construction in part (a) by selecting an arbitrary
point A on the curve y = x³. Show that the two areas R and
S are always related in the same way.

Transcribed Image Text:

B 64 48 32 16 y RT S 2 C {y=x³ A(1, 1) 4 -X