Question
Find the acute angles between the curves at their points of intersection. (The angle between two curves is the angle between their tangent lines at the point of intersection.)$ y = x^2 $ , $ y = x^3 $
Step 1
We do this by setting $y = x^2$ equal to $y = x^3$ and solving for $x$. This gives us $x^2 = x^3$ or $x^2 - x^3 = 0$. Factoring out $x^2$ gives $x^2(1 - x) = 0$. Setting each factor equal to zero gives $x = 0$ and $x = 1$. Substituting these values back into Show more…
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