SOLUTION: find the coordinates of the two points on the curve y=2x^3-5x^2+9x-1 at which the gradient of the tangent is 13. I dont know how to factor the cubic equation (i tried division by i

Algebra ->  Rational-functions -> SOLUTION: find the coordinates of the two points on the curve y=2x^3-5x^2+9x-1 at which the gradient of the tangent is 13. I dont know how to factor the cubic equation (i tried division by i      Log On


   

Question 881085: find the coordinates of the two points on the curve y=2x^3-5x^2+9x-1 at which the gradient of the tangent is 13. I dont know how to factor the cubic equation (i tried division by inspection but I didnt get anywhere) and I dont know how to find the coordinates.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
To find the slope of the tangent, take the derivative.
y=2x%5E3-5x%5E2%2B9x-1
dy%2Fdx=6x%5E2-10x%2B9
Set the value of the derivative (slope of the tangent) equal to 13,
6x%5E2-10x%2B9=13
6x%5E2-10x-4=0
3x%5E2-5x-2=0
%283x%2B1%29%28x-2+%29=0
Two solutions:
3x%2B1=0
3x=-1
x=-1%2F3
and
x-2=0
x=2
Now go back to the original equation and calculate the y coordinate for each given x solution.