JEE Main 2023 — Application of Derivatives Questions with Solutions

If f x = x 2 + g ' 1 x + g " 2 and g x = f 1 x 2 + x f ' x + f " x , then the value of f 4 - g 4 is equal to __…

A wire of length 20   m is to be cut into two pieces. A piece of length ℓ 1 is bent to make a square of area…

The number of points, where the curve y = x 5 - 20 x 3 + 50 x + 2 crosses the x -axis, is _____.

The absolute minimum value, of the function f x = x 2 - x + 1 + x 2 - x + 1 , where t denotes the greatest integer func…

Let f x = 1 + sin 2 x cos 2 x sin 2 x sin 2 x 1 + cos 2 x sin 2 x sin 2 x cos 2 x 1 + sin 2 x ,   x ∈ π…

Let x = 2 be a local minima of the function f x = 2 x 4 - 18 x 2 + 8 x + 12 , x ∈ - 4 , 4 . If M is local maximum…

max 0 ≤ x ≤ π x - 2 sin x cos x + 1 3 sin 3 x =

The sum of the abosolute maximum and minimum values of the function f x = x 2 - 5 x + 6 - 3 x + 2 in the interval - 1 ,…

If a α is the greatest term in the sequence a n = n 3 n 4 + 147 ,   n = 1 ,   2 ,   3 . . . . , the…

Let the tangent to the curve x 2 + 2 x - 4 y + 9 = 0 at the point P 1 , 3 on it meet the y - axis at A . Let the line p…