Question

Find the coordinates of the point on the curve y=x^2-3x+1 where gradient is:-5

Answer 1

`y=f\left( x \right) \\ \\ f\left( x \right) ={ x }^( 2 )-3x+1\\ \\ \therefore \quad f'\left( x \right) =2x-3`

Now, when f'(x)=-5,


`2x-3=-5\\ \\ 2x=-2\\ \\ x=-1`

When x=-1,


`f\left( -1 \right) ={ \left( -1 \right) }^( 2 )-3\left( -1 \right) +1\\ \\ =1+3+1\\ \\ =5`

Therefore, the co-ordinates you're looking for are:

(-1, 5)