How do you find the local extrema for $f(x)=-0.12x^3 + 900x - 830$ ?

Question

1327 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-22T08:20:47

local max. at $(50, 29170)$
local min. at $(-50, -30830)$

$f(x) = -.12x^3 + 900x -830$

Find the first derivative: $f'(x) = -.36x^2+900$

Find the critical numbers ( $f'(x) = 0$ ):

$.36x^2 = 900; x^2 = 2500; x = +-50$

Second derivative test:

$f''(x) = -.72x;$

$f''(-50) > 0$ ; relative min at $x = -50$ and $f(-50) = -30,830$

$f''(50) < 0$ ; relative max at $x = 50$ and $f(50) = 29,170$

local max. at $(50, 29170)$
local min. at $(-50, -30830)$

How do you find the local extrema for f(x)=-0.12x^3 + 900x - 830f(x)=-0.12x^3 + 900x - 830?