Application of Derivatives

Find the slope of the tangent to the curve . - Wired Faculty

Question

Find the slope of the tangent to the curve $straight y space equals fraction numerator straight x minus 1 over denominator straight x minus 2 end fraction comma space space space straight x not equal to space 2 space space at space straight x space equals space 10$ .

Solution

The equation of curve is
$straight y space equals space fraction numerator straight x minus 1 over denominator straight x minus 2 end fraction comma space space space space space space straight x space not equal to space 2$
$therefore space space space space space space dy over dx space equals space fraction numerator left parenthesis straight x minus 2 right parenthesis. space begin display style straight d over dx end style left parenthesis straight x minus 1 right parenthesis minus left parenthesis straight x minus 1 right parenthesis begin display style straight d over dx end style left parenthesis straight x minus 2 right parenthesis over denominator left parenthesis straight x minus 2 right parenthesis squared end fraction space space space space space space space space space space space space space space space space space space space space equals space fraction numerator left parenthesis straight x minus 2 right parenthesis. space 1 minus space left parenthesis straight x minus 1 right parenthesis. space 1 over denominator left parenthesis straight x minus 2 right parenthesis squared end fraction space equals space fraction numerator straight x minus 2 minus straight x plus 1 over denominator left parenthesis straight x minus 2 right parenthesis squared end fraction space equals space minus fraction numerator 1 over denominator left parenthesis straight x minus 2 right parenthesis squared end fraction At space straight x space equals space 10 comma space space space dy over dx space equals space minus fraction numerator 1 over denominator left parenthesis 10 minus 2 right parenthesis squared end fraction space equals space minus 1 over 64$
which is required slope of tangent to the curve.

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Application Of Derivatives

Find the slope of the tangent to the curve $straight y space equals fraction numerator straight x minus 1 over denominator straight x minus 2 end fraction comma space space space straight x not equal to space 2 space space at space straight x space equals space 10$ .

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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