DeterminantHard
Question
Let f(x) = 
, then
, thenOptions
A.f(x) is independent of x
B.f′(π/2) = 0
C.
D.tangent to the curve y = f(x) at x = 0 is y = 0
Solution
f(x) = 
= 2 sin x (4 sin2x - sin2x) - sin2x(2sin x) = 6sin3x - 2sin3x
f(x) = 4 sin3x
f′(x) = 12sin2x cos x
(B) f′(π/2) = 12 sin2 (π/2) cos (π/2) = 0
(C) f(-x) = - f(x) odd function
∴
= 0
(D) at x = 0, y = 0
= 0 tangent at (0, 0)
y - 0 =
(x - 0)
y = 0
= 2 sin x (4 sin2x - sin2x) - sin2x(2sin x) = 6sin3x - 2sin3x
f(x) = 4 sin3x
f′(x) = 12sin2x cos x
(B) f′(π/2) = 12 sin2 (π/2) cos (π/2) = 0
(C) f(-x) = - f(x) odd function
∴
= 0(D) at x = 0, y = 0
= 0 tangent at (0, 0) y - 0 =
(x - 0)y = 0
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