Mathematics I20805 marksNumerical: increasing decreasing intervalsCurve sketching
Find where the function f(x) = 3x4 - 4x3 - 12x2 + 5 is increasing and where it is decreasing.
Find where the function $f(x) = 3x^4 - 4x^3 - 12x^2 + 5$ is increasing and where it is decreasing. [5]
- $f(x) = 3x^4 - 4x^3 - 12x^2 + 5$ $$f'(x) = 12x^3 - 12x^2 - 24x$$ $$12x^3 - 12x^2 - 24x = 0$$ $$12x(x^2 - x - 2) = 0$$ $$12x(x-2)(x+1) = 0$$ $$x = -1,\ 0,\ 2$$ Interval Test $12x$ $(x-2)$ $(x+1)$ $f'(x)$ Behaviour --------------------- $(-\infty,-1)$ $x=-2$ $-$ $-$ $-$ $-$ Decreasing $(-1,0)$