For the function, f x = e x cos ⁡ x , x ∈ 0 , 2 π , the slope of the tangent at any point on the curve of the function is minimum at

Step-by-step solution

f x = e x cos ⁡ x f ' x = - e x sin ⁡ x + e x cos ⁡ x f ' x = e x cos ⁡ x - sin ⁡ x Let g x = e x cos ⁡ x - sin ⁡ x is the slope of the tangent to the curve, then, g ' x = e x - sin ⁡ x - cos ⁡ x + e x cos ⁡ x - sin ⁡ x = e x - sin ⁡ x - cos x ⁡ + cos ⁡ x - sin ⁡ x g ' x = - 2 e x sin ⁡ x   ⇒   x = 0 ,   π ,   2 π So it is minima at x = π