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 = 4x2, y = 4x3

Answer 1

Answer:

Step-by-step explanation:

Given that there are two curves

$y =4x^2\\y=4x^3$

Eliminate y to get intersection as x=0,1

Thus points of intersection are (0,0) and (1,4)

$Derivative = 8x, 12x^2\\Slope at (0,0) = 0,0\\Slope at (1,4) = 8, 12$

Thus x axis is one tangent for both.

Next is

$y-4 = 8(x-1) \\ y-4= 12(x-1)\\y=8x-4\\y =12x-8$

m1 =8 and m2 =12

Angle between the lines is

tan t = $\frac{12-8}{1+12(8)} =\frac{4}{97}$

Angle = tan inverse of 4/97