Example 2-3-9 - Maple Help



Chapter 2: Space Curves



Section 2.3: Tangent Vectors



Example 2.3.9



Given the two plane curves $f\left(x\right)={x}^{2},g\left(x\right)=8-{\left(\frac{x}{4}\right)}^{2},x\ge 0$,

 a) At $x=1$, obtain the equation of the line tangent to $y=f\left(x\right)$.
 b) Find the coordinates of the intersection of $y=g\left(x\right)$ and the tangent line found in Part (a).
 c) Construct a vector from $\left(1,f\left(1\right)\right)$ to the point found in Part (b).
 d) Obtain $\mathbf{R}\prime \left(1\right)$, the natural tangent vector at $\left(1,f\left(1\right)\right)$.
 e) Show that the vectors in Parts (c) and (d) are parallel. (Hint:  Show their components are proportional.)
 f) Draw both curves, the tangent line (Part (a)), and the tangent vector (Part (d)).