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Question

The minimum value of f(x) = -2 x2 + 5x + 4 ∀ x [0, 3] is __

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Solution

f(x) = -2x2 + 5x + 4

a < 0 ⇒ Graph of f(x) will have maximum value at x = b2a = 54

As 0 < (54) < 3, minimum of f(0) & f(3) will be minimum value of f(x) in x [0, 3]

So, f(0) = 4

f(3) = -18 + 15 + 4 = 1

so, f(3) = 1 is minimum value


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