Maxima and MinimaMedium
Question
Read of the following mathematical statements carefully :
I. A differentiable function ′f′ with maximum at x = c ⇒ f″(c) < 0.
II. Anti derivative of a periodic function is also a periodic function.
III. If f has a period T then for any a ∈ R,
f (x)dx = 
f (x + a)dx
IV. If f(x) has a maxima at x = c, then ′f′ is increasing in (c - h, c ) and decreasing in (c, c + h) as h → 0 for h > 0
Now indicate the correct alternative.
I. A differentiable function ′f′ with maximum at x = c ⇒ f″(c) < 0.
II. Anti derivative of a periodic function is also a periodic function.
III. If f has a period T then for any a ∈ R,
f (x)dx = f (x + a)dxIV. If f(x) has a maxima at x = c, then ′f′ is increasing in (c - h, c ) and decreasing in (c, c + h) as h → 0 for h > 0
Now indicate the correct alternative.
Options
A.exactly one statement is correct
B.exactly two statements are correct
C.exactly three statements are correct
D.all the four statements are correct
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