Application of Derivatives questions
910 published questions with worked solutions.
- By dropping a stone in a quiet lake, a wave in the form of circle is generated. The radius of the circular wave increases at the...
- The angle between the curves xy=6 and x^2y=12 is
- In the mean value theorem, f'(c)= f(b)-f(a) b-a , if a=0, b= 12 and f(x)=x(x-1)(x-2), then the value of c is
- If the rate of increase of surface area of a spherical balloon is 5 , cm ^ 2 /sec and rate of increase of volume of a spherical...
- Rolle's theorem holds for quadratic polynomial f(x) on the interval [ , +3]. Similarly, g(x)=f(x)+2 also follows Rolle's theorem...
- The value of c satisfied by the Rolle's theorem for the function f(x)=x^2(1-x)^2,x [0,1] is…
- A tank with a rectangular base and rectangular sides, open at the top is made. Depth of the tank is 4 m and its volume is 36...
- A manufacturer produces x items per week at a total cost of Rs (x^2 + 78x + 2500). The price per unit is given by 8x = 600 - p...
- If 2f(x) + 3f ( 1 x ) = x^2 + 1, x 0 and y = 5x^2 f(x), then y is strictly increasing in
- If the curve y = ax^2 - 6x + b passes through (0, 4) and has its tangent parallel to the x-axis at x= 3 2 , then the value of a...
- 20 is divided into two parts so that the product of the cube of one part and the square of the other part is maximum, then those...
- The function f(x)=x(x+3)e^ - ( 12 )x satisfies all the conditions of Rolle's theorem in [-3,0], then c=
- The line x+y=0 touches the curve y^2=ax^3+b at (1,-1) then values of respectively are …
- An aeroplane at an altitude of 1 km is flying horizontally at 600 km / hry passes directly over an observer. Then the rate at...
- If the line ax+by+5=0 is a normal to the curve xy=1 then….
- The abscissae of the points of the curve y=x^3 are in the interval [-2, 2], where the slope of the tangents can be obtained by...
- Let x be the length of each of the equal sides of an isosceles triangle and be the angle between these sides. If x is increasing...
- A wire of length 8 units is cut into two parts which are bent respectively in the form of a square and a circle. The least value...
- Angle between the parabola y^2=4(x-1) and x^2+4(y-3)=0 at the common end of their latus rectum is
- If f(x)= k x+2 x x+ x is strictly increasing for all real x, then
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