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
Deepak Pandey
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)#

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