JEE Mains Model Paper 4

we have , y = −x3 + 3x2 +x -27
∴

dy

dx

= −3x2 +6x + 9 = slope of tangents to the curve
Now ,

d2y

dx2

= -6x + 6
For

d

dx

(

dy

dx

) = 0 , x = 1
Also

d

dx

(

d2y

dx2

) = -6 < 0
So, the slope of tangents to the curve is maximum , where x = 1 The required point of is (1,-16)