Class 12

Math

Calculus

Application of Derivatives

Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

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If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume.

Find the approximate value of $f(5.001)$, where $f(x)=x_{3}−7x_{2}+15$.

Find the intervals in which the function f given by $f(x)=x_{2}−4x+6$is (a) strictly increasing (b) strictly decreasing

Find local maximum and local minimum values of the function f given by$f(x)=3x_{4}+4x_{3}−12x_{2}+12$.

Find the intervals in which the function f given by $f(x)=x_{3}+x_{3}1 ,x=0$is (i) increasing (ii) decreasing.

Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.

Find the intervals in which the function f given by $f(x)=4x_{3}−6x_{2}−72x+30$is (a) strictly increasing (b) strictly decreasing