(ii) g ( x ) = x – x (iii) h ( x ) = sin x + cos x , (iv) f ( x ) = sin x – cos x , < π (v) f ( x ) = x – x + x + (vi) g x > (vii) g x (viii) , f x . Prove that the following functions do not have maxima or minima: (i) f ( x ) = e x (ii) g ( x ) = log x (iii) h ( x ) = x + x + x + . Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: (i) f ( x ) = x , x ∈ [– , ] (ii) f ( x ) = sin x + cos x , x ∈ [ , π ] (iii) f ( x ) = , ∈− (iv) ) , [ , ] f x ∈− . Find the maximum profit that a company can make, if the profit function is given by p ( x ) = – x – x .
Find both the maximum value and the minimum value of x – x + x – x + on the interval [ , ]. . At what points in the interval [ , π ], does the function sin x attain its maximum value? .
What is the maximum value of the function sin x + cos x ? . Find the maximum value of x – x + in the interval [ , ]. Find the maximum value of the same function in [– , – ].
. It is given that at x = , the function x – x + ax + attains its maximum value, on the interval [ , ]. Find the value of a . .