Maxima and MinimaHard
Question
f(x) is cubic polynomial which has local maximum at x = - 1. If f(2) = 18, f(1) = - 1 and f′(x) has local minima at x = 0, then
Options
A.the distance between (-1, 2) and (a, f(a)), where x = a is the point of local minima is 2√5
B.f(x) is increasing for x ∈ [1, 2√5]
C.f(x) has local minima at x = 1
D.the value of f(0) = 5
Solution
The required polynomial which satisfy the condition
is f(x) =
(19x3 - 57x + 34)f(x) has local maximum at x = - 1 and local minimum at x = 1
Hence f(x) is increasing for x ∈ [1, 2√5]
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