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)