Project ForgeEngineering Mathematics
Calculus
GATE 2007
Easy
Consider the following two statements about the function f(x) = |x|: P. f(x) is continuous for all real values of x. Q. f(x) is differentiable for all real values of x. Which of the following is TRUE?
- P is true and Q is false.
- BP is false and Q is true.
- CBoth P and Q are true.
- DBoth P and Q are false.
Explanation
f(x) = |x| is continuous everywhere — there's no jump or break at any point, including x=0, where the left and right limits both equal 0. But it is NOT differentiable at x=0: the left-hand derivative there is −1 and the right-hand derivative is +1, so the derivative doesn't exist at that corner. Hence P is true and Q is false.
Source: GATE CS 2007 (2007)
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