AP EAMCET202419 May 2024Evening ShiftMathematicsContinuity and DifferentiabilityActual
Let f (x)= x, x^2 for every real number of x . then
Options
- Af(x) is continuous for all x
- Bf(x) is differentiable for all x
- Cf^ (x)=2 for all x 1
- Df(x) is not differentiable at three values of x
Correct answer
A. f(x) is continuous for all x
Step-by-step solution
aligned f(x) & = x, x^2 & = array ccc x & if & x 0 x^2 & if & 0 x 1 x & if & 1 x array . aligned _ x 0⁻ f(x)= _ x 0⁻ x=0 Similarly, we can show _ x 0⁺ f(x)=0 So, f(x) is continuous at x=0 Similarly f(x) is also continuous at x=1 and f^ (x)= array cc 1, & x 0 2 x, & 0 x 1 1, & x 1 array . So, f(x) is not differentiable at x=0,1 .