Application of Derivatives
If the sum of the hypotenuse and a side of a right angled triangle is given, show that the area of the triangle is maximum when the angle between them is 3π˙
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The length x of a rectangle is decreasing at the rate of 3 cm/minute and the width y is increasing at the rate of 2cm/minute. When x=10cm and y=6cm, find the rates of change of (a) the perimeter and (b) the area of the rectangle.
Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 2%.
Find the equation of the normal to curve x2=4ywhich passes through the point (1, 2).
Let f be a function defined on [a, b] such that fprime(x)>0, for all x∈(a,b). Then prove that f is an increasing function on (a, b).
A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?
Find the maximum and the minimum values, if any, of the function f given byf(x)=x2,x∈R.
Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is tan−12.
For all real values of x, the minimum value of 1+x+x21−x+x2is(A) 0 (B) 1 (C) 3 (D) 31