which the slope of the tangent is − ? ( ) − ( ) − ( ) − ( ) . The slope of the line normal to the curve f x = at x = π is ( ) − ( ) − ( ) ( ) . The tangent to the curve y is vertical when ( ) y = ( ) y = ± ( ) y = ( ) y = ± .
Angle between y = and x = at the origin is ( ) tan − ( ) tan − ( ) p ( ) p . The value of the limit lim cot is ( ) ( ) ( ) ( ) ∞ - - Applications of Differential Calculus . The function sin is increasing in the interval ( ) ( ) π ( ) π π ( ) , π . The value of ‘c’ satisfied by the Rolle’s theorem for the function f x [ , ] is ( ) ( ) ( ) ( ) .
The value of ‘c’ satisfied by the mean value theorem for the function f x [ , ] is ( ) ( ) . ( ) ( ) . . The minimum value of the function f x | | is ( ) ( ) ( ) ( ) .
The maximum slope of the tangent to the curve y x x sin , [ , ] π is at ( ) x = π ( ) x = π ( ) x = π ( ) x = . The maximum value of the function f x x e > is ( ) ( ) e ( ) e ( ) e . One of the closest points on the curve x to the point ( , ) is ( ) ( ,