Answer:
Step-by-step explanation:
From the information,
equation of curve = y^2 = 2x^3
equation of line = 4x - 3y + 1 = 0
The first step is to find the slope of the line. Recall, the equation of a line in the slope intercept form is expressed a
y = mx + c
where
m represents slope
We would rearrange the given equation. We have
3y = 4x + 1
y = 4x/3 + 1/3
Thus,
m = 4/3
The slope of the perpendicular line = - 1/m = - 3/4
For the curve, we would find the derivative.
y = (2x^3)^1/2
y' = 2^3/2 * x^3/2
f'(x) = (3√x)/√2
We would equate the derivative to the slope of the perpendicular line. We have
(3√x)/√2 = - 3/4
3√x * 4 = - 3√2
12√x = - 3√2
√x = - 3√2/12
√x = -√2/4
Square both sides
x = (-√2/4)^2 = 2/16
x =
Substituting x = 1/8 into y = (2x^3)^1/2, we have
y = (2(1/8)^3)^1/2
y = √256
y =