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Application Of Derivatives

Question
CBSEENMA12035074
Wired Faculty App

Find the point at which the tangent to the curve straight y equals space square root of 4 straight x minus 3 end root space minus 1 has its slope 2 over 3.

Solution

The equation of curve is
                         straight y space equals space square root of 4 straight x minus 3 end root space minus space 1 space equals space left parenthesis 4 straight x minus 3 right parenthesis to the power of 1 half end exponent space minus space 1
therefore space space space space space space dy over dx space equals space 1 half left parenthesis 4 straight x minus 3 right parenthesis to the power of 1 half end exponent space 4 space minus 0 space equals space fraction numerator 2 over denominator square root of 4 straight x minus 3 end root end fraction.
which is slope of tangent to the curve.
From given condition.
               dy over dx space equals space 2 over 3 space space space space space space space or space space space space space space space fraction numerator 2 over denominator square root of 4 straight x minus 3 end root end fraction space equals space 2 over 3 space space space space rightwards double arrow space space space space fraction numerator 1 over denominator square root of 4 straight x minus 3 end root end fraction space equals space 1 third rightwards double arrow space space space space space square root of 4 straight x minus 3 end root space equals space 3 space space rightwards double arrow space space space space 4 straight x minus 3 space equals space 9 space space space space space space space rightwards double arrow space space space space 4 straight x space equals space 12 space space space space space space rightwards double arrow space space space space space straight x space equals space 3 When space straight x space equals 3 comma space space space straight y space equals space square root of 4 space cross times 3 minus 3 end root space minus 1 space equals space square root of 9 space minus space 1 space equals space 3 minus 1 space equals space 2 therefore space space space space space required space point space is space left parenthesis 3 comma space 2 right parenthesis.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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