If `f(x)=x^5-5x^4+5x^3-10` has local maximum and minimum at `x=pa n dx=q` , respectively, then `(p , q)-=` `(0,1)` (b) (1,3) (c) (1,0) (d) none of these

If f(x)=x+(1)/(x),xne0 , then local maximum and minimum values of function f are respectively . . .

If the function f(x)=2x^(3)-9ax^(2)+12x^(2)x+1, where a>0, attains its maximum and minimum at p and q, respectively,such that p^(2)=q, then a equal to (a) 1 (b) 2 (c) (1)/(2) (d) 3

If x^(3)+(1)/(x^(3))=110, then x+(1)/(x)=5 (b) 10 (c) 15 (d) none of these

If the function f(x)=x^3-12ax^2+36a^2x-4(agt0) attains its maximum and minimum at x=p and x=q respectively, and if 3p=q^2 , then a is equal to

If f(x)=|x-3| and g(x)= fof (x), then for x>10,g'(x) is equal to (a)1(b)-1(c)0 (d) none of these

Let f(x)=int_0^xe^(-t^2)(t-5) (t^2-7t+12) dt for all x in (0, oo) then (A) f has a local maximum at x = 4 and a local minimum at x=3 (B) f is decreasing on (3,4)(5, oo) and increasing on (0,3) (4,5). (C) There exists atleast two c_1, c_2 in (0, oo) such that f"(c_1)=0 and f"(c_2)=0. (D) There exists some c in (0, oo) such that f"'(c) = 0

Find the local maximum and local minimum value of f(x)= x^(3)-3x^(2)-24x+5

f(x)=int_0^x e^-t^2(t-5)(t^2-7t+12)dt for all x in (0,oo) then (A) f has local maximum at x=4 and a local minimum at x=3 (B) f is decreasing on (3,4)uu(5,oo) and inccreasing on (0,3)uu(4,5) (C) There exists atleats two c_1,c_2 in (0,oo) such that f''(c_1)=0 and f''(c_2)=0 (D) There exists some c in (0,oo) such that f'''(c)=0

If 2f(x)-3f((1)/(x))=x^(2)(x!=0), then f(2) is equal to (a)-(7)/(4)(b)(5)/(2)(c)-1 (d) none of these