Question

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?

Answer 1

`(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)`