JEE Main 2020 — Application of Derivatives Questions with Solutions

Let P h ,   k be a point on the curve y = x 2 + 7 x + 2 , nearest to the line, y = 3 x - 3 . Then the equation of…

Let f x = x cos - 1 ⁡ - sin ⁡ x , x ∈ - π 2 , π 2 , then which of the following is true?

If the lines x + y = a and x - y = b touch the curve y = x 2 - 3 x + 2 at the points where the curve intersects the x -…

The function, f x = 3 x - 7 x 2 3 ,   x ∈ R , is increasing for all x lying in

If x = 1 is a critical point of the function f ( x ) = 3 x 2 + a x - 2 - a e x , then

Let f : - 1 , ∞ → R be defined by f 0 = 1 and f x = 1 x log e 1 + x ,   x ≠ 0 . Then the functio…

The position of a moving car at time t is given by f ( t ) = a t 2 + b t + c ,   t > 0 , where a ,   b &#…

Suppose f x is a polynomial of degree four having critical points at - 1 ,   0 ,   1 . If T = x ∈ R &#1…

If the surface area of a cube is increasing at a rate of 3 . 6 c m 2 / s e c , retaining its shape; then the rate of ch…

If the tangent to the curve y = e x at a point c ,   e c and the normal to the parabola y 2 = 4 x at the point 1 ,…