Let `S` denote the set of all polynomials `P(x)` of degree `lt=2` such that `P(1)=1,P(0)=0a n dP^(prime)(x)>0AAx in [0,1]` , then `S=varphi` b. `S={(1-a)x^2+a x ;0

If P(x) is a polynomial of degree 3 satisfying p(-1)=10 ,p(1)=-6a n dp(x) has maxima at x=-1a n dp^(prime)(x) has minima at x=1, find the distance between the local maxima and local minima of the curve.

consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1 and lim_(xrarr0) p(x)/(x^(3))-2=4 Then the value of P(x)_____.

Let f(x) be the fourth degree polynomial such that f^(prime)(0)=-6,f(0)=2 and (lim)_(x->1)(f(x))/((x-1)^2)=1 The value of f(2) is a. 3 b. 1 c. 0 d. 2

Let f(x)=x^(3)+x+1 , let p(x) be a cubic polynomial such that the roots of p(x)=0 are the squares of the roots of f(x)=0 , then

p(x) is a polynomial of degree 1 and q(x) is a polynomial of degree 2. What kind of the polynomial p(x) xx q(x) is ?

Let p(x) be a real polynomial of least degree which has a local maximum at x=1 and a local minimum at x=3. If p(1)=6a n dp(3)=2, then p^(prime)(0) is_____

If varphi(x) is a polynomial function and varphi^(prime)(x)>varphi(x)AAxgeq1a n dvarphi(1)=0, then varphi(x)geq0AAxgeq1 varphi(x)

Let f: R-> be a differentiable function AAx in R . If the tangent drawn to the curve at any point x in (a , b) always lies below the curve, then (a) f^(prime)(x)<0,f^(x)<0AAx in (a , b) (b) f^(prime)(x)>0,f^(x)>0AAx in (a , b) (c) f^(prime)(x)>0,f^(x)>0AAx in (a , b) (d) non eoft h e s e

If S_(1) and S_(2) are respectively the sets of local minimum and local maximum point of the function, f(x)=9x^(4)+12x^(3)-36x^(2)+25, x in R , then (a) S_(1)={-2}:S_(2)={0,1} (b) S_(1)={-2,0}:S_(2)={1} (c) S_(1)={-2,1}:S_(2)={0} (d) S_(1)={-1}:S_(2)={0,2}