Question

Estimate to the nearest 0.5 unit and classify the extrema for the graph of each function.

Answer 1

$f(x) = x^3+x^2-x$

Finding the extreme point :

$f'(x)=3x^2+2x-1=0\\\\3x^2+3x-x-1=0\\\\3x(x+1)-1(x+1)=0\\\\(3x-1)(x+1)=0\\\\x=\dfrac{1}{3}\ ,\ x=-1$

Now,

f''( x ) at x = 1/3 and -1 is :

$f''(x)=6x+2\\\\f''(1/3)=4 \\\\f''(-1)=-4$

Therefore, it is maximum at x = -1 and minimum at x = 1/3 .

Hence, this is the required solution.