Assertion (A): No value of $k$ makes $f(x) = \lvert x - 2 \rvert + kx$ differentiable at $x = 2$ .
Reason (R): Adding $kx$ adds the same $k$ to both one-sided derivatives at $x = 2$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

R is true: the one-sided derivatives at 2 are $k - 1$ and $k + 1$ .
They differ by 2 whatever $k$ is, so they are never equal: A is true, and R is why.

Worth noting

Adding a line tilts both slopes of the corner equally and cannot close the gap between them.

Concept: When no constant makes a function differentiable
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsDifferentiability

Practise this chapter →

Ten questions from Continuity & Differentiability, at your own pace.

Assertion (A): No value of kkk makes f(x)=∣x−2∣+kxf(x) = \lvert x - 2 \rvert + kxf(x)=∣x−2∣+kx differentiable at x=2x = 2x=2.Reason (R): Adding kxkxkx adds the same kkk to both one-sided derivatives at x=2x = 2x=2.

Explanation

Assertion (A): No value of $k$ makes $f(x) = \lvert x - 2 \rvert + kx$ differentiable at $x = 2$ .
Reason (R): Adding $kx$ adds the same $k$ to both one-sided derivatives at $x = 2$ .