Given the function defined by f(x) = x^5-5x^4+3, find all the values of x for which the graph of f is concave up?
回答 (3)
2015-12-16 2:06 pm
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2015-12-16 1:47 pm
Well,
f(x) = x^5 - 5x^4 + 3
f '(x) = 5x^4 - 20x^3
f "(x) = 20x^3 - 60x^2
f is concave up at point x iif f "(x) > 0
and here :
f "(x) = 20x^3 - 60x^2 = 20x^2 (x - 3)
f "(x) > 0 <==> x > 3
conclusion : f is concave up on (3, +oo)
hope it' ll help !!
f(x) = x^5 - 5x^4 + 3
f '(x) = 5x^4 - 20x^3
f "(x) = 20x^3 - 60x^2
f is concave up at point x iif f "(x) > 0
and here :
f "(x) = 20x^3 - 60x^2 = 20x^2 (x - 3)
f "(x) > 0 <==> x > 3
conclusion : f is concave up on (3, +oo)
hope it' ll help !!
2015-12-16 3:13 pm
f(x) = x^5 -5x^4 +3. f'(x) = 5x^4 - 20x^3. f''(x) = 20x^3 - 60x^2 = 20x^2(x-3). For graph
of f(x) to be concave upwards, we require f''(x) > 0 which holds on (3 , + inf).
of f(x) to be concave upwards, we require f''(x) > 0 which holds on (3 , + inf).
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