Jamia Millia Islamia MCA Application Of Derivatives Previous Year Questions (PYQs)
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The point of inflection for $f(x) = 3x^4 - 4x^3$ are –
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Solution
Solution:
$f'(x) = 12x^3 - 12x^2$
$f''(x) = 36x^2 - 24x = 12x(3x - 2)$
Set $f''(x) = 0 \Rightarrow x = 0,\ x = \dfrac{2}{3}$
Hence, points of inflection are $x = 0$ and $x = \dfrac{2}{3}.$
The side of an equilateral triangle is increasing at the rate of $2\ \text{cm/s}$.
The rate at which area increases when the side is $10\ \text{cm}$ will be —
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Solution
For an equilateral triangle, area $A = \dfrac{\sqrt{3}}{4}s^2$
Differentiate with respect to time $t$:
$\dfrac{dA}{dt} = \dfrac{\sqrt{3}}{2}s\dfrac{ds}{dt}$
Given $\dfrac{ds}{dt} = 2$ and $s = 10$,
$\dfrac{dA}{dt} = \dfrac{\sqrt{3}}{2} \times 10 \times 2 = 10\sqrt{3}$
Hence, rate = $10\sqrt{3}$ cm$^2$/s
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