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If f(x) = x⁴ + 3x² then at x = 2 arrange the following in descending order of their value : (i) f(x)…

At \(x = 2\) for \(f(x) = x^4 + 3x^2\): (i) \(f(2) = 16 + 12 = 28\); (ii) \(f'(x) = 4x^3 + 6x \implies f'(2) = 32 + 12 = 44\); (iii) \(f''(x) = 12x^2 + 6 \implies f''(2) =…

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If f(x) = x⁴ + 3x² then at x = 2 arrange the following in descending order of their value :
(i) f(x)
(ii) f'(x) = (d/dx)(x⁴ + 3x²)
(iii) f''(x) = (d²/dx²)(x⁴ + 3x²)
(iv) x⁵

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Answer and explanation

Correct answer A

At x=2x = 2 for f(x)=x4+3x2f(x) = x^4 + 3x^2: (i) f(2)=16+12=28f(2) = 16 + 12 = 28; (ii) f′(x)=4x3+6x  ⟹  f′(2)=32+12=44f'(x) = 4x^3 + 6x \implies f'(2) = 32 + 12 = 44; (iii) f′′(x)=12x2+6  ⟹  f′′(2)=48+6=54f''(x) = 12x^2 + 6 \implies f''(2) = 48 + 6 = 54; (iv) x5=25=32x^5 = 2^5 = 32. Descending order is 54>44>32>2854 > 44 > 32 > 28, i.e., (iii) > (ii) > (iv) > (i).

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