Applications of Derivatives
Subject matter experts of JagranJosh have developed chapter wise practice questions of Class 12th as per the relevancy of the chapter in the CBSE board exam. This practice set contains 10 questions with detailed explanations on “Chapter: Applications of Derivatives” of Mathematics.

Q1.The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. At, x = 8 cm and y = 6 cm, which of the following options is correct?
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Q2.$$\begin{array}{l}Find\text{}the\text{}points\text{}on\text{}the\text{}curve\text{}{x}^{2}+{y}^{2}\text{}2x\u2013\text{}3\text{}=\text{}0\text{}\\ at\text{}which\text{}the\text{}tangents\text{}are\text{}parallel\text{}to\text{}x\text{}axis.\end{array}$$
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Q3.$$\begin{array}{l}Find\text{}the\text{}points\text{}on\text{}the\text{}curvey={x}^{3}at\text{}which\text{}the\text{}slope\text{}of\text{}the\text{}tangent\text{}is\text{}equal\text{}to\text{}\\ theycoordinate\text{}of\text{}the\text{}point.\end{array}$$
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Q4.A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at the rate of 0.05 cm/s. The rate at which its area is increasing when radius is 3.2 cm is
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Q5.$$\begin{array}{l}It\text{}is\text{}given\text{}that\text{}atx=\text{}1,\text{}the\text{}function{x}^{4}\text{}62{x}^{2}+ax+\text{}9\text{}attains\text{}its\text{}maximum\text{}value,\\ on\text{}the\text{}interval\text{}\left[0,\text{}2\right].\text{}Find\text{}the\text{}value\text{}ofa.\end{array}$$
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Q6.Find the rate of change of the area of a circle with respect to its radius r when r = 4 cm
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Q7.If a =1,then$$the\text{}function\text{}{x}^{2}+a\text{}x+1\text{}on\text{}interval\text{}\left(1,\text{}1\right)\text{}is$$
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