Application of Derivatives questions
910 published questions with worked solutions.
- The equation of the tangent to the curve y = 3x^3 - 3x^2 + x at x = 1 is
- The approximate value of [3] 63 is
- A wire of length 64 m is so to be bent to form a rectangle such that its area is maximum then its area is
- The difference between the local extreme values of the function f(x) = 2x^3 - 15x^2 + 36x + 40 is
- At present a firm is manufacturing 1000 items. It is estimated that the rate of change of production P w.r.t. additional number...
- The equation of the tangent to the curve y= 9-2x^2 , at the point where the ordinate and abscissa are equal, is
- If a and b are positive numbers such that a>b, then the minimum value of a -b (0< < 2 ) is
- A rod AB, 13 feet long moves with its ends A and B on two perpendicular lines OX and OY respectively. When A is 5 feet from O, it...
- If y=a x+bx^ 2 +x has its extreme values at x=-1 and x=2, then the value of ( b + b ) is
- The curve y=ax^ 3 +bx^ 2 +cx+5 touches the X-axis at (-2,0) and cuts the Y-axis at a point Q where its gradient is 3, then values...
- If the normal to the curve y=f(x) at the point (3, 4) makes an angle of ( 3 4 ) with the positive X-axis, then the value of f'(3)...
- Let f(x)= x a^ 2 +x^ 2 - d-x b^ 2 +(d-x)^ 2 , x IR where a, b, d are non-zero real constants. Then
- If f(x)=x^ 3 -6x^ 2 +9x+3 is monotonically decreasing function, then x lies in
- If equation of normal to the curve x= t , y=t- 1 t at t=4 is
- The approximate value of (3.978)^ 3 2 is
- A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that melts at the rate of 50 cm^3 / min....
- If the function f(x)=x^3-3(a-2)x^2+3ax+7, for some a IR is increasing in (0,1] and decreasing in [1,5). Then a root of the...
- On the interval [0, 1] the function x^ 25 (1-x)^ 75 takes its maximum value at the point
- The equation of the normal to the curve 3x^2 - y^2 = 8, which is parallel to the line x + 3y = 10, is
- A ladder, 5 meters long, rests against a vertical wall. If its top slides downwards at the rate of 10 cm/s, then the angle...
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