Question

Find the coordinates of the point on the curve y=3x^2 – 9x +8 at which the inclination of the tangent is 45°​

Answer 1

Answer:

(5/3 , 4/3) and (4/3 , 4/3)

Explaination:

y = 3 x² - 9 x + 8

dy/dx = m = slope of tangent at (x,y) = 6x - 9

internal angle is 45 deg.

If the tangent is in quadrant 1 or 3, then slope = -1 ie., angle is 135 deg.  

If the tangent is in quadrant 2 or 4, then slope = 1 ie, angle is 45 deg.

   

So the points:

  m = 1,   6x - 9 = 1     => x = 5/3   => y = 3 (5/3)² - 9 *5/3 +8 = 4/3

  m = -1,  6x - 9 = -1    => x = 4/3   =>  y = 3 (4/3)² - 9*4/3 +8 = 4/3

I HOPE THIS WILL HELP YOU OUT!!