Question:
The sides of an equilateral triangle are increasing at the rate of 4 cm/sec. The rate at which its area is increasing, when the side is 14 cm.
The sides of an equilateral triangle are increasing at the rate of 4 cm/sec. The rate at which its area is increasing, when the side is 14 cm.
Updated On: Apr 17, 2024
- 42 $cm^2 / \sec$
- $ 10\sqrt{3} cm^2 / \sec$
- 14 $cm^2 / \sec$
- $ 14 \sqrt{3} cm^2 / \sec$
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The Correct Option is B
Solution and Explanation
$\frac{dx}{dt}=4cm/ sec,$ $x = 14cm$
$A=\frac{\sqrt{3}}{4} x^{2}$
$\frac{d A}{d t}=\frac{\sqrt{3}}{4} \times 2x \frac{d x}{d t}$
$=\frac{\sqrt{3}}{2}\times14\times4$
$=\sqrt{3}\times7\times4$
$=28\sqrt{3}$
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Concepts Used:
Continuity & Differentiability
Definition of Differentiability
f(x) is said to be differentiable at the point x = a, if the derivative f ‘(a) be at every point in its domain. It is given by
Definition of Continuity
Mathematically, a function is said to be continuous at a point x = a, if
It is implicit that if the left-hand limit (L.H.L), right-hand limit (R.H.L), and the value of the function at x=a exist and these parameters are equal to each other, then the function f is said to be continuous at x=a.
If the function is unspecified or does not exist, then we say that the function is discontinuous.