If `f(x)= ax^2-b, |x|<1 ` and `f(x)=-1/|x|, |x|>=1` is derivable at `x=1` then find values of `a` and `b`

If the function f(x) given by f(x)={(3a x+b,"if "x >1), (11,"if "x=1), (5a x-2b ,"if "x<1):} is continuous at x=1 then find the values of a and b.

f(x)={ax^(2)-b,, if |x| =1 is differentiable at x=1, find a,bquad if |x|>=1

If the function f(x) given by f(x)={3ax+b,quad if x>1quad if quad if x=15ax-2b,quad if x is continuous at x=-1, find the values of a and b

If the function f(x) = axe^(bx^(2)) has maximum value at x=2 such that f(2) =1 , then find the values of a and b

Let f(x)=lim_(n rarr oo)(x^(2n-1)+ax^(2)+bx)/(x^(2n)+1). If f(x) is continuous for all x in R then find the values of a and b.

If f(x)=x^(3)-x^(2)+ax+b is divisible by x^(2)-x, then find the value of f(2)

If lim_(xtooo) {(x^(2)+1)/(x+1)-(ax+b)}=0, then find the values of a and b.

If lim_(x rarr oo){(x^(2)+1)/(x+1)-(ax+b)}=0, then find the value of a and b.

If f(x)={{:(a+bx,xlt1),(4,x=1),(b-ax,xgt1):} and underset(xrarr1)f(x)=f(1) , then find the values of 'a' and 'b '

For the function f(x)=x^(3)-6x^(2)+ax+b , it is given that f(1) = f(3) = 0. Find the values of 'a' and 'b', and hence, verify Rolle's Theorem on [1, 3].