if p(x) be a polynomial of degree 3 satisfying p(-1) = 10 , p(1) = -6  and p(x) maximum at x = -1 and  p'(x) minima at  x = 1.

find the distace between the local maximum and local minimum of the curve.

 let the equation be f(x)= ax³+bx²+cx+d..

Give f(-1)=10=>  -a+b-c+d=10

f(1)=-6=>a+b+c+d=-6    =>b+d=2

                                               a+c=-8

also maxima of f(x) at x=-1

=>f'(-1)=0( f('x)=3ax²+2bx+c)   or 3a-2b+c=0

and minima of f'(x) at x=1

=>f"(1)=0(f"(x)=6ax+2b)    or 6a+2b=0 or b=-3a   =>a=1,b=-3,c=-9 and d=5

hence substitute and find

if you want i can work that too:)