For which a and b is f(x) = x^3 if x ≤ 2; ax + b if x > 2 differentiable at x = 2?

Continuity & Differentiability · Question 115 of 125

Question 115

HardOriginal question

For which $a$ and $b$ is $f(x) = \begin{cases} x^{3}, & x \le 2 \\ ax + b, & x > 2 \end{cases}$ differentiable at $x = 2$ ?

a = 4,\ b = 0

Correct answerYour answer

a = 12,\ b = 8

Correct answerYour answer

a = 12,\ b = -16

Correct answerYour answer

a = 6,\ b = -4

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Worth noting

$a = 4,\ b = 0$ only joins the values at 2; the slope of $x^{3}$ there is $3x^{2} = 12$ .

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

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