Maximum value of the function y = x^3 − 3 + 2 is?
Answers
Answer:
Find the minimum and maximum values of the function y=x
3
−3x
2
+6. Also find the values of x at which these occur.
Step-by-step explanation:Given y=x
3
−3x
2
+6
Differentiating y w.r.t. x,
dx
dy
=3x
2
−6x
Putting dy/dx=0, we get the values at which the function is maximum or minimum. So
3x
2
−6x=0
⇒x(3x−6)=0⇒x=0,+2
To distinguish the values of x as the point of maximum or minimum, we need second derivative of the function.
∴
dx
2
d
2
y
=6x−6; Now (
dx
2
d
2
y
)
x=0
=−6<0.
So x=0 is a point of maximum.
Similarly, (
dx
2
d
2
y
)
x=+2
=6>0
So x=+2 is a point of minimum.
Hence, the maximum value of y is 0
3
−3×0+6=6 and the minimum value of y is (2)
3
−3(2)
2
+6=2.
HOPE THIS ANSWER HELPFUL