Application of Derivatives questions
910 published questions with worked solutions.
- If y = 4x - 5 is a tangent to the curve y^2 = px^3 + q at (2, 3), then p - q is
- The diagonal of a square is changing at the rate of 0.5 cm/sec. Then the rate of change of area when the area is 400 cm^2 is...
- Let P(x) be a polynomial of degree 2, with P(2) = -1, P'(2) = 0, P''(2) = 2, then P(1.001) is
- Let the curve be represented by x=2( t+t t), y=2( t-t t). Then normal at any point 't' of the curve is at a distance of..........
- Let B (0,3) and C (4,0). The point A is moving on the line y=2x at the rate of 2 units/second. The area of ABC is increasing at...
- Let f(x)= x^2-3x+2 x^4+1 dx, then function decreases in the interval
- The point on the curve 9y^2=x^3 where the normal to the curve makes equal intercepts with the co-ordinate axes is
- The approximate value of (0.007)^ 13 is
- The maximum value of ( 1x )^x, x>0 is
- The surface area of a spherical ball is increasing at the rate of 4 cm^2/second. The rate at which the radius is increasing when...
- The co-ordinates of the point on the curve y=x x at which the normal is parallel to the line 2x-2y=3 are..
- If the function f(x)=ax^3-bx^2-8x-4 satisfies Roll's theorem in [1,3], if f'(2)=0 then a-b is equal to ….
- If f(x)=x^ 3 -10x^ 2 +200x-10, then
- A ladder 5 m in length is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the...
- The approximate value of 3^ 2.001 , if 3=1.0986 is
- The equation of tangent to the curves x=1-3t^2 and y=t-3t^3 at the point (-2,2) is...
- A spherical snow ball is melting so that its volume is decreasing at the rate of 8 c.c./sec then the rate of change of radius...
- A cylindrical tank without a top lid is being manufactured to hold a fixed volume of 125 cubic cm. The minimum surface area...
- The minimum value of x x in the interval (2, ) is
- The function f(x)= ^ -1 ( x+ x) is an increasing function in the interval….
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