Let f x = 2 x - x 2 , x ∈ R . If m and n are respectively the number of points at which the curves y = f x and y = f ' x intersects the x - axis, then the value of m + n is

Step-by-step solution

Given, Function f x = 2 x - x 2 , x ∈ R Now, plotting the diagram of y = 2 x & y = x 2 we get, Now, from above diagram total point of intersection are three ∴ m = 3 Now, finding f ' ( x ) = 2 x ln 2 - 2 x = 0 2 x ln 2 = 2 x Now, again plotting the diagram of y = 2 x ln 2 & y = 2 x we get, So, from above diagram total point of intersection is two ∴ n = 2 Hence, m + n = 5