Question

Calculus

Answer 1

@SithsAndGiggles

Answer 2

For x > 0, f'(x) is positive. So f(x) must be increasing
For x < 0, f'(x) is negative. So f(x) must be decreasing
f'(0) = 0 so it is maxima/minima of f(x)
That is all I got so far.

Answer 3

You can also use the extrema of \(f'(x)\) to determine the concavity of \(f(x)\).

Answer 4

yeah thanks! @ranga
@sithgiggles , that's what i'm going to ask.. what's the use of the extrema of f'(x), how to use it?

Answer 5

For this particular function, \(f'(x)\) has extrema at \(x=-1\) and \(x=1\); a minimum and maximum, respectively.

A minimum means \(f'(x)\) is decreasing to the left of \(x\) and increasing to the right of \(x\). This tells you that \(f''(x)<0\) to the left of \(x\) and \(f''(x)>0\) to the right of \(x\). This in turn tells you that \(f(x)\) is concave down and up, respectively.

Note the difference:

Answer 6

ok got it thanks!!! (^_^)

Answer 7

you're welcome!