Application of Derivatives
If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its volume.
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Find ′c of Lagrange's mean-value theorem forf(x)=(x3−3x2+2x) on [0,21]
Find the intervals in which the function f given by f(x)=2x3−3x2−36x+7 is (a) strictly increasing (b) strictly decreasing.
Find the least value of a such that the function f given by f(x)=x2+ax+1 is strictly increasing on [1,2].
Using Rolle's theorem, find the point on the curve y=x(x−4),xϵ[0,4], where the tangent is parallel to the x-axis
Using differentials, find the approximate value of :329
Verify Lagranges's mean-value theorem for the following function:f(x)=x3+x2−6x on [−1,4]
Find the maximum of minimum values, if any, without using derivation, of the functions:−(x−3)2+9
An open box with a square base to be made out of a given cardboard of area c2 (square) units. Show that the maximum volume of the box is 63c3 (cubic units.)