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

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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)#