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Find the maximum and minimum values of f (x) = 2x3 – 24x + 107 in the interval [1, 3].
- a)89, 69
- b)89, 75
- c)59, 56
- d)89, -9
Correct answer is option 'B'. Can you explain this answer?
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Find the maximum and minimum values of f (x) = 2x3– 24x + 107 in...
Toolbox:d/dx(x^n) = nx^n−1Maxima & Minima = f′
(x) = 0Step 1:f(x) = 2x^3−24x+107Differentiating with
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Find the maximum and minimum values of f (x) = 2x3– 24x + 107 in...
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Find the maximum and minimum values of f (x) = 2x3– 24x + 107 in...
f(x)=2x³-24x+107 x ∈ [1, 3]
f'(x) = 6x^2 - 24
To find the points equate f'(x) = 0
in closed interval x= -2 doesn't lies,so discard x = -2
now find the value of function at x = 1, 2 ,3
f(1) =2(1)³-24(1)+107
= 2-24+107 = 85
f(2) =2(2)³-24(2)+107
= 16-48+107 = 75
f(3) =2(3)³-24(3)+107
= 54-72+107 = 89
So, the function has maximum value in close interval at x= 3, Maximum value= 89.
minimum value at x= 2, minimum value = 75
f'(x) = 6x^2 - 24
To find the points equate f'(x) = 0
in closed interval x= -2 doesn't lies,so discard x = -2
now find the value of function at x = 1, 2 ,3
f(1) =2(1)³-24(1)+107
= 2-24+107 = 85
f(2) =2(2)³-24(2)+107
= 16-48+107 = 75
f(3) =2(3)³-24(3)+107
= 54-72+107 = 89
So, the function has maximum value in close interval at x= 3, Maximum value= 89.
minimum value at x= 2, minimum value = 75
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Find the maximum and minimum values of f (x) = 2x3– 24x + 107 in the interval [1, 3].a)89, 69b)89, 75c)59, 56d)89, -9Correct answer is option 'B'. Can you explain this answer?
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