Question

The maximum and minimum value of the function Y is equal to x^ 3 X^2+6 is

Answer 1

let f(x)=x³+x²+6
differentiate with respect to x.
f'(x)=3x²+2x
let f'(x)=0
3x²+2x=0
3x²=-2x
x=-2/3,0
again differentiate with respect to x.
f"(x)=6x+2
case1) when x=0
f"(0)=2>0
therefore,x=0 is point of minima.
f(0)=0³+0²+6=6.
maximum value of f(x) is 6 at x=0
case2) when x=-2/3
f''(-2/3)=-4+2=-2<0.
therefore,x=-2/3 is called point of Maxima.
f(-2/3)=-8/27+4/9+6={-8+12+162}/27
=166/7=6.148
Maximum value of f(x) is 6.148 at x=-2/3.
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