Question

Find the points on the curve y = 3 x square - 9 X + 8 at which the tangents are equally inclined with the axes

Answer 1

Step-by-step explanation:

Given the curve is y=3x^2−9x+8.

Now Dy/dy=6x−9.....(1)

The slope of the tangent to the given curve at (x,y) is Dy/dx

If the tangent at (x,y) is equally inclined to the axes then the slope of the tangent at that point is 1.

Then from (1) we've,

6x−9=1

or, 6x=10

or, x= 5/3

Since the point lies on the given curve then for x= 5/3 we've,

y=3× 25/9-9×5/3

or, y= 25/3-45/3+8

or, y= 4/3

So the point is (5/3,4/3)