Which of these describes f(x) = x^2 if x ≤ 1; 2x - 1 if x > 1 at x = 1?

Continuity & Differentiability · Question 95 of 125

Question 95

MediumOriginal question

Which of these describes $f(x) = \begin{cases} x^{2}, & x \le 1 \\ 2x - 1, & x > 1 \end{cases}$ at $x = 1$ ?

Continuous but not differentiableCorrect answerYour answerNeither continuous nor differentiableCorrect answerYour answerDifferentiable but not continuousCorrect answerYour answerContinuous and differentiableCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Both pieces give 1 at $x = 1$ : continuous.
The slopes are $2x = 2$ and 2: equal, so differentiable.

Worth noting

A change of formula is smooth when both the values and the slopes match.

Concept: Testing differentiability at a point
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsDifferentiability

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Which of these describes f(x)={x2,x≤12x−1,x>1f(x) = \begin{cases} x^{2}, & x \le 1 \\ 2x - 1, & x > 1 \end{cases}f(x)={x2,2x−1,​x≤1x>1​ at x=1x = 1x=1?

Explanation

Which of these describes $f(x) = \begin{cases} x^{2}, & x \le 1 \\ 2x - 1, & x > 1 \end{cases}$ at $x = 1$ ?