Question

What point is the tangent line to the curve y =x^3 +5 perpendicular to the line x+3y=2

Answer 1

I got the slope of the normal line and points of tangency. I don't know what I need to do next..

Answer 2

I'm not really sure with my points of tangency tho

Answer 3

Slope of the line x + 3y = 2 is -1/3
So the slope of the perpendicular line is 3 ( product slopes should be -1)
This is required slope of the tangent line

From the given curve equation, y = x^3 + 5,
Slope of the tangent line for this curve is dy / dx = 3.x^2
This slope should be 3,
So 3.x^2 = 3
x^2 = 1
x = +1,-1
Substituting these values of x in the curve equation we get,
the two points (1,6) and (-1,4)

Answer 4

ooh so we can equate the slope of the tangent line of the curve and the slope of the normal line?

Answer 5

i mean perpendicular line?

Answer 6

Yes you are right

Answer 7

Thank you so much!

Answer 8

I have another question related to this.

Answer 9

why do we have to substitute our point of tangency to the curve and not on the equation of the line?