Sketch-the-graph-of-the-function-f-is-defined-by-f-x-x-4-8x-3-clearly-giving-all-the-properties-used-in-it-

Question Number 11288 by agni5 last updated on 19/Mar/17

Sketch the graph of the function f is defined

by f (x) = x^{4} + {8 x}^{3}, clearly giving all the

properties used in it .

Answered by ajfour last updated on 19/Mar/17

Commented by ajfour last updated on 19/Mar/17

f (x) = x^{4} + {8 x}^{3} = x^{3} (x + 8)

at x = 0, - 8 f (x) = 0

f^{^{'}} (x) = {4 x}^{3} + {24 x}^{2} = {4 x}^{2} (x + 6)

\Rightarrow f^{^{'}} (x) = 0 at x = 0, 0, - 6

f^{^{″}} (x) = 12 x (x + 4)

\Rightarrow point of inflexion at x = 0, - 4

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