JEE Main 2021 — Application of Derivatives Questions with Solutions

A wire of length 20   m is to be cut into two pieces. One of the pieces is to be made into a square and the other…

Let a be a real number such that the function f ( x ) = a x 2 + 6 x - 15 , x ∈ R is increasing in - ∞ , 3 4…

Let a curve y = f x pass through the point 2 , log e 2 2 and have slope 2 y x log e x for all positive real values of x…

If R is the least value of a such that the function f x   =   x 2   +   a x   +   1 is in…

Let a be an integer such that all the real roots of the polynomial 2 x 5 + 5 x 4 + 10 x 3 + 10 x 2 + 10 x + 10 lie in t…

Let f x be a cubic polynomial with f 1 = - 10 ,   f - 1 = 6 , and has a local minima at x = 1 , and f ' x has a lo…

If the area of the triangle formed by the x -axis, the normal and the tangent to the circle x - 2 2 + y - 3 2 = 25 at t…

The minimum value of α for which the equation 4 sin x + 1 1 - sin x = α has at least one solution in 0 , &#96…

Let M and m respectively be the maximum and minimum values of the function f ( x ) = tan - 1 ( sin x + cos x ) in 0 , &…

Let f : R → R be defined as f x = - 55 x , if   x < - 5 2 x 3 - 3 x 2 - 120 x , if - 5 ≤ x ≤…