Find the equation of the normal to the curve y= 2x\(^2\) - 5x + 10 at P(1, 7)

A.

y+x-3 =0

B.

y-x+6=0

C.

y - x - 6=0

D.

y -x+ 3 =0

Correct answer is C

From y= 2x- 5x 10 ; dy/dx= 4x-5

But at (1, 7); m\(_1\) = (dy/dx)\(_{1,7}\)

= 4(1) - 5 = -1

Using m\(_1\)m\(_2\),= -1; m\(_2\) = 1.

Gradient m\(_2\), of normal at (1,7) is 1.

Using y - y\(_1\) = m(x - x\(_1\))

y - 7 = 1(x - 1) ;

y - 7 = x - 1

y - x - 6 = 0