Application of Derivatives
If length of three sides of a trapezium other than base are equal to 10cm, then find the area of the trapezium when it is maximum.
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Find ′c of Lagrange's mean-value theorem forf(x)=25−x2 on [1,5]
The radius of a circle is increasing at the rate of 0.7cm/s. What is the rate of increase of its circumference?
Show that Lagrange's mean-value theorem is not applicable to f(x)=∣x∣ on [−1,1].
Find the points on the curve y=x3 at which the slope of the tangent is equal to the y coordinate of the point.
If the length of a simple pendulum is decreased by 2%, find the percentage decrease in its period T, where T=2πgl.
Prove that the function f given by f(x)=logsinx is strictly increasing on (0,2π) and strictly decreasing on ( 2π,π )
Verify Lagranges's mean-value theorem for the following function:f(x)=tan−1x on [0,1]
Find the rate of change of the area of a circle with respect to its radius r when(i) r=3 cm(ii) r=4 cm