Question

find the absolute maximum value and the absolute minimum value of the function f(X)=4x-1/2x^2 x£(-2,9/2)
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Answer 1

We have to find the absolute maximum and absolute minimum of the function, f(x) = 4x - 1/2 x² where x ∈ (-2, 9/2)

Solution : differentiating f(x) with respect to x,

f'(x) = 4 - x

at f'(x) = 0 ⇒x = 4

now find value of f(x) at x = -2, 4, and 9/2

so, f(-2) = 4(-2) - 1/2 (-2)² = -8 - 2 = -10

f(4) = 4(4) - 1/2 (4)² = 16 - 8 = 8

F(9/2) = 4(9/2) - 1/2 (9/2)² = 18 - 81/8 = (144 - 81)/8 = 63/8 = 7.875

Here we see that absolute minimum value of function f(x) is -10 and absolute maximum value of f(x) is 8.

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