I need help with this problem: At what value of x do the graphs of y=x^(2) and y=-sqrt (x) have perpendicular tangent lines?

Question

Choices (a) -1 (b) 0 (c) 1/4 (d) 1 (e) none

Answer 1

At what value of x do the graphs of y=x^(2) and y=-sqrt (x) have perpendicular tangent lines?

Let m1 = slope of y = x^2

i.e. m1 = y' = 2x

Let m2 = slope of y = -sqrt(x)

i.e. m2 = y' = -(1/2)/sqrt(x)

These two slopes will be perpindicular when m1*m2 = -1

So, (2x)*(-(1/2)/sqrt(x)) = -1

-x/sqrt(x) = -1

x = sqrt(x)

The solution here is: x = 0 or x = 1