Let: `f(x)=int_0^x|2t-3|dtdot` Then discuss continuity and differentiability of `f(x)a tx=3/2`

Discuss the differentiability of f(x)=|x^3| at x=0

Discuss the differentiability of f(x)="max"{x^2-3x+2,2-|x-1|}

Let f(x)=x^3-3x^2+6AAx in R and g(x)={m a x :f(t ; x+1lt=tlt=x+2,-3lt=xlt=0 1-x ,xgeq .Find continuity and differentiability of g(x) for x in [-3,1]

Let f(x)=int_(2)^(x)f(t^(2)-3t+4)dt . Then

Discuss the differentiability of f(x)={(sinx^2)/x ,x!=0 0,x=0a tx=0

Discuss the differentiability of f(x)=|x|sinx+|x-2|sgn(x-2)+|x-3|dot

Discuss the continuity of f(x)={(x^2)/(|x|),x!=0 0,x=0

Let f:[0,2]->R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1 L e t :F(x)=int_0^(x^2)f(sqrt(t))dtforx in [0,2]dotIfF^(prime)(x)=f^(prime)(x) . for all x in (0,2), then F(2) equals (a) e^2-1 (b) e^4-1 (c) e-1 (d) e^4

Discuss the continuity of f(x)=sgn(x^3-x)

Let f(x)=1/x^2 int_0^x (4t^2-2f'(t))dt then find f'(4)