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  •  If     <img alt="f(x)=\left\{\begin{array}{r} |x-4|, \text { for } x \geq 1 \\ \left(x^3 / 2\right)-x^2+3 x+(1 / 2), \text { for } x<1 \end{array}\right. \text {, then }" sr

 If     f(x)=\left\{\begin{array}{r} |x-4|, \text { for } x \geq 1 \\ \left(x^3 / 2\right)-x^2+3 x+(1 / 2), \text { for } x<1 \end{array}\right. \text {, then }

Option: 1

f(x) is continuous at x=1 and at x=4


Option: 2

f(x) is differentiable at x=4


Option: 3

f(x) is continuous and differentiable at x=1


Option: 4

f(x) is only continuous at x=1


Answers (1)

best_answer

\mathrm{\text {We have: } f(x)=\left\{\begin{array}{c} x-4, x \geq 4 \\ -(x-4), 1 \leq x<4 \\ \left(x^3 / 2\right)-x^2+3 x+(1 / 2), x<1 \end{array}\right.}

Clearly, f(x) is continuous for all x but it is not differentiable at x=1 and x=4.

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Rishi

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