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 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+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

The number of real solutions of the (log)_(0. 5)|x|=2|x| is (a) 1 (b) 2 (c) 0 (d) none of these

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 local maximum and local minimum of f(x) = 2x^(3) + 5x^(2) - 4x

Solve: x^3-5x^2+5x-1=0

Find the local maximum and minimum values of the following functions 2x^(3)+5x^(2)-4x

The range of the function f(x)=|x-1|+|x-2|,-1lt=xlt=3, is [1,3] (b) [1,5] (c) [3,5] (d) none of these

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. It 'a is a root of x^2-x-6=0

The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent, if the straight line 35 x-22 y+1=0 passes through the point (a) (a , b) (b) (b ,a) (c) (-a ,-b) (d) none of these