Application of DerivativeHard
Question
Let f(x) = 40/(3x4 + 8x3 - 18x2 + 60). Which of the following statement(s) about f(x) is (are) correct ?
Options
A.f(x) has local minima at x = 0.
B.f(x) has local maxima at x = 0.
C.Absolute maximum value of f(x) is not defined.
D.f(x) is local maxima at x = - 3, x = 1.
Solution
f′(x) = 
f′(x) = 0
at x = 0, x = - 3, x = 1
so at x = 0, f(x) has local minima.
and at x = - 3, x = 1 ; f(x) has local maxima
f(1) =
f(- 3) = 
. f(-3) < 0, f(1) > 0 and f(x) ≠ 0
⇒ f(x) is undefined at point(s) in (-3, 1). Hence f(x) has no absolute maxima.
f′(x) = 0
at x = 0, x = - 3, x = 1
so at x = 0, f(x) has local minima.
and at x = - 3, x = 1 ; f(x) has local maxima
f(1) =
f(- 3) = . f(-3) < 0, f(1) > 0 and f(x) ≠ 0⇒ f(x) is undefined at point(s) in (-3, 1). Hence f(x) has no absolute maxima.
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