Application of Derivatives questions
910 published questions with worked solutions.
- The number of distinct real roots of the equation 3x^4+4x^3-12x^2+4=0 is ____
- Let M and m respectively be the maximum and minimum values of the function f(x) = ^ -1 (sinx+cosx) in [0, 2 ], then the value of...
- A box open form top is made from a rectangular sheet of dimension a × b by cutting squares each of side x from each of the four...
- The number of real roots of the equation e^ 4x +2e^ 3x -e^x-6=0 is :
- If 'R' is the least value of 'a' such that the function f(x) = x^2 + ax + 1 is increasing on [1, 2] and 'S' is the greatest value...
- The shortest distance between the line x – y = 1 and the curve x^2=2y is :
- The minimum value of f(x)=a^ a^x +a^ 1-a^x , where a, x R and a > 0, is equal to :
- If the curves x = y^4 and xy = k cut at right angles, then (4k)^6 is equal to _______.
- If the curves, x^2 a + y^2 b =1 and x^2 c + y^2 d =1 intersect each other at an angle of 90°, then which of the following...
- If Rolle's theorem holds for the function f(x)=x^3-ax^2+bx-4, x [1, 2] with f' ( 4 3 )=0, then ordered pair (a, b) is equal to :
- Let f(x)=3 ^4x+10 ^3x+6 ^2x-3, x [ 6 , 2 ]. Then, f is :
- The local maximum value of the function f(x)= ( 2 x )^ x^2 , x > 0, is
- Let a and b respectively be the points of local maximum and local minimum of the function f(x)=2x^3-3x^2-12x. If A is the total...
- The maximum slope of the curve y= 1 2 x^4-5x^3+18x^2-19x occurs at the point
- The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of...
- For the function f(x) = 4 _ e (x - 1) - 2x^ 2 + 4x + 5, x > 1, which one of the following is NOT correct ?
- If the tangent at the point (x_ 1 , y_ 1 ) on the curve y = x^ 3 + 3x^ 2 + 5 passes through the origin, then (x_ 1 , y_ 1 ) does...
- The sum of absolute maximum and absolute minimum values of the function f(x) = |2x^ 2 + 3x − 2| + sin x cos x in the interval [0,...
- Let _ 0 x 2 9 - x^2 5 - x = and _ 0 x 2 9 - x^2 5 - x = . If _ - 83 ^ 2 -1 9-x^2 5-x , x dx = _1 + _2 _e ( 8 15 ) then _ 1 + _ 2...
- Let x, y > 0. If x^ 3 y^ 2 = 2^ 15 , then the least value of 3x + 2y is
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