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

The function f(x)=x^(5)-5x^(4)+5x^(3) find maximum and minimum value

If the function f(x)=2x^3-9ax^2+12a^2x+1, where a gt 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=? (a) 5 (b) 10 (c) 15 (d) none of these

If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal to (a)0 (b) 1/(14) (c) -1/4 (d) None of these

The coefficient of x^3 in the expansion of (1-x+x^2)^5 is (a). -83 (b). 0 (c) .^(30)C_(10) (d). none of these

If the maximum and minimum values of y=(x^2-3x+c)/(x^2+3x+c) are 7 and 1/7 respectively then the value of c is equal to (A) 3 (B) 4 (C) 5 (D) 6

The function f(x)=sqrt(a x^3+b x^2+c x+d) has its non-zero local minimum and local maximum values at x=-2 and x = 2 , respectively. If a is a root of x^2-x-6=0 , then find a,b,c and d.

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

At x=(5pi)/6,\ \ f(x)=2sin3x+3cos3x is (a) 0 (b) maximum (c) minimum (d) none of these

At x=(5pi)/6,\ \ f(x)=2sin3x+3cos3x is (a) 0 (b) maximum (c) minimum (d) none of these