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. Give your answers in degrees, rounding to one decimal place. Enter your answers as a comma-separated list.)
y = 6x2,
y = 6x3
I know that they intersect at (1, 6) and I already took the derivatives to find that the slope of the tangent lines are 12 and 18. What do I do now?

Answer 1

Answer:

Step-by-step explanation:

To find the acute angles between the curves at their points of intersection, we find the angle between the tangents to the curve  at their points of intersection.

$y = 6x^2,y = 6x^3$

I know that they intersect at (1, 6)

Here given that the tangents have slopes as

$m_1 =12\\m_2 =18$

So angle between the curves = angles between the two tangents

=$tan \theta =|\frac{m_1-m_2}{1+m_1m_2} |\\=\frac{8}{1+216} \\\theta = 2.1113$ degrees

Thus angle between the curves is 2.113 degrees or arc tan (8/217)