Set, Relation and FunctionMedium

Question

Let f(x) = (3z - z2 - 4)dz has the same domain as g(x) = sec-1 (1 + ), then (Æ’(x)max - Æ’(x)min) is -

Options

A.
B.
C.
D.

Solution

d dd         dDomain of g(x)
8x - x2 - 15 ≥ 0 ⇒ [3,5]
f′(x) = 3x– x2 - 4
f′(x) < 0 ∀ x ∈ [3,5]
f(x)max = f(3), f(x)min = f(5)
f(5) =
f(3) = -
⇒ f(3) – f(5) =

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