Application of Derivatives
Using Lagranges mean value theorem, prove that bb−a<log(ab)<ab−a=a,where 0<a<b˙
The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3cm/s˙ How fast is the area decreasing when the two equal sides are equal to the base?
Find the maximum value and the minimum value and the minimum value of 3x4−8x3+12x2−48x+25 on the interval [0,3]˙
In an acute triangle ABC if sides a,b are constants and the base angles AandB vary, then show that a2−b2sin2AdA=b2−a2sin2BdB
The tangent to the parabola y=x2 has been drawn so that the abscissa x0 of the point of tangency belongs to the interval [1,2]. Find x0 for which the triangle bounded by the tangent, the axis of ordinates, and the straight line y=x02 has the greatest area.