If `f(x)={a x^2-b ,\ \ \ if\ |x|<1 1/(|x|),\ \ \ \ \ \ \ \ \ \ \ \ if\ |x|geq1` is differentiable at `x=1` , find `a ,\ bdot`

The function f(x) is defined by f(x)={x^2+a x+b\ \ \ ,\ \ \ 0lt=x 4 f is continuous them determine the value of a and b

The function f(x) is defined by f(x)={x^2+a x+b\ \ \ ,\ \ \ 0lt=x 4 f is continuous them determine the value of a and b

If f(x)=A x^2+B x+C then find f '(x)

If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,where ac !=0, then prove that f(x)g(x)=0 has at least two real roots.

If f(x)=(x-a)^2(x-b)^2 , find f(a+b)

If f(x)=x^3+a x^2+b x+c has a maximum at x=-1 and minimum at x=3 . Determine a ,\ b and c .

If f(x)={x ,\ xlt=1x^2+b x+c ,\ x >1 , then find the values of b\ a n d\ c if f(x) differentiability at x=1.

Let f(x)=a x^(2)+b x+c , a, b, in R, a neq 0 satisfying f(1)+f(2)=0 . Then the equation f(x)=0 has

If f(x)=a x^2+b x+c is a quadratic function such that f(1)=8,f(2)=11 and f(-3)=6 find f(x) by using determinants. Also, find f(0)dot