If the function `f(x)=2x^3-9ax^2+12x^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 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

Find the maximum and minimum values, if any, of the functions given by f(x) = 9x^(2) + 12x + 2

Find the maximum and minimum values, if any, of the functions given by f (x) = (2x – 1)^(2)+ 3

If the normals to the parabola y^2=4a x at P meets the curve again at Q and if P Q and the normal at Q make angle alpha and beta , respectively, with the x-axis, then t a nalpha(tanalpha+tanbeta) has the value equal to 0 (b) -2 (c) -1/2 (d) -1

If the function f(x)=a x^3+b x^2+11 x-6 satisfies conditions of Rolles theorem in [1,3] and f'(2+1/(sqrt(3)))=0, then values of a and b , respectively, are (A) -3,2 (B) 2,-4 (C) 1,-6 (D) none of these

It is given that at x = 1, the function x^(4) – 62x^(2) + ax + 9 attains its maximum value, on the interval [0, 2]. Find the value of a.

For the equation 3x^2+p x+3=0,p >0, if one of the root is square of the other, then p is equal to 1/3 (b) 1 (c) 3 (d) 2/3

If range of function f(x)=sin^(-1)x+2tan^(-1)x+x^2+4x+1 is [p , q], then the value of (p+q) is_______>

The function f(x)=x/2+2/x has a local minimum at x=2 (b) x=-2 x=0 (d) x=1

Find the constant C such that the function f(x)=C(2x+3x^(2))1lt xlt 3 =0 otherwise is a density functino and compute P(1le x lt2)