Application of Derivatives

4. Examine for max. and min. the following: (1) a tanx + b xot x . (ii) cos'x , sin x bz (ii) a sinx + bcos x. (iv) (5+x)(2+x). 1+x (v) 1+x+x 1-x+x2 5. Show that the following functions have the functions have neither maximum nor minimum value: (i) x3 - 9x2 + 94x - 7 (ii) 4x3 - 18x2 + 27x - 7. (uil) cot=1x, tan-1x (iv) tanx, cot x. 5 . Show that for x = e (i) xx is a max. * is a min. 6 . (i) Prove that the a seco seco + b cosec 0 is a min. when tan 0 = (91 8 . Find when 1+3x VIEri 's a max. 9. The graph of y = (x-1)(x-4) ax+ has a turning point at P(2, -1) Determine the value of a and b and show that y is a maximum at P. 10 . What is a point of flections Find the point if inflexion for the curve aly = (x - b)3. 11 . Find the max. Value of. (i) xy Under the condition x + y = a. (ii) xy When xty = 5. 12 . Show that the function sin"x cos"x attains its max. value at o where tan of = LAI's