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8.03 Differentiation by first principles

Interactive practice questions

Which of the following functions are differentiable over their entire domain?

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A

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B

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C

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D
Easy
< 1min

Consider the graph of the function $f\left(x\right)=2x+2$f(x)=2x+2 shown below.

Easy
2min
Consider the graph of the function $f\left(x\right)$f(x) $=$= $-x^2+4$x2+4 when $x\ge0$x0
$x^2+4$x2+4 when $x<0$x<0
Easy
1min
Consider the graph of the function $f\left(x\right)$f(x) $=$= $\frac{x^3-x}{x^2-1}$x3xx21 when $x\ne\pm1$x±1
$1$1 when $x=-1$x=1
$4$4 when $x=1$x=1
Easy
< 1min
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Outcomes

MA11-1

uses algebraic and graphical techniques to solve, and where appropriate, compare alternative solutions to problems

MA11-5

interprets the meaning of the derivative, determines the derivative of functions and applies these to solve simple practical problems

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