Solve mcq and also explain the gradient?

the point at which curve y=x^2-4x+6
has gradient -2 is
a.(0,1)
b.(1,0)
c.(2,1)
d.(-3,2)
which is correct answere and how?

1 Answer
Aug 15, 2017

(1,3)

Explanation:

Gradient means slope i.e the slope of the tangent on any point on the curve.

Suppose the tangent to any point on the curve makes angle theta with the positive direction of the x axis then the gradient of the curve at that point is given by dy/dx= tantheta

Now in our case
y=x^2-4x+6
=>dy/dx=2x-4
Now as dy/dx=-2 is given
:.2x-4=-2
:.x=1
Putting. x=1 in the equation of curve we get y=3
:. The point is (1,3)