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Statistics 2 Marks Each

DIFFERENTIATION · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 54 questions.

Questions · Page 2 of 2

2 Marks Each

Question 512 Marks
Determine whether the function $y=12+4x-7x^{2}$ is increasing or decreasing at $x=2$.
Answer
$\frac{dy}{dx} = 4 - 14x$.
At $x = 2, \frac{dy}{dx} = 4 - 14(2) = 4 - 28 = -24$.
Since $\frac{dy}{dx} < 0$, the function is decreasing at $x = 2$.
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Question 522 Marks
Define elasticity of demand.
Answer
Elasticity of demand is the ratio of the relative (percentage) change in demand to the relative (percentage) change in price. If x is demand and p is price, elasticity $\eta = -\frac{p}{x} \cdot \frac{dx}{dp}$.
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Question 532 Marks
If $ f(x)=x^{2}-x+3 $ then for which value of x, $ f'(x)=0 $ ?
Answer
$ f'(x) = 2x - 1 $
Set $ f'(x) = 0 $ :
$ 2x - 1 = 0 $
$ 2x = 1 $
$ x = 0.5 $
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Question 542 Marks
If $f(x)=4 x^3+2 x^2+7 x+9$, then for which value of $x, f^{\prime \prime}(x)=52$ ?
Answer
$f'(x) = 12x^2 + 4x + 7$
$f''(x) = 24x + 4$
Given $24x + 4 = 52 \implies 24x = 48 \implies x = 2$.
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2 Marks Each - Page 2 - Statistics STD 12 Commerce Questions - Vidyadip