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

Sagot :

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

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

[tex]2x-3=-5\\ \\ 2x=-2\\ \\ x=-1[/tex]

When x=-1,

[tex]f\left( -1 \right) ={ \left( -1 \right) }^{ 2 }-3\left( -1 \right) +1\\ \\ =1+3+1\\ \\ =5[/tex]

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

(-1, 5)
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