Application of Derivatives
The line y=mx+1 is a tangent to the curve y2=4x if the value of m is(A) 1 (B) 2(C) 3(D) 1/2.
A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is (a32+b32)23.
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.
The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base ?