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10.02 Tangents and their equations

Interactive practice questions

Consider the curve $f\left(x\right)$f(x) drawn below along with $g\left(x\right)$g(x), which is a tangent to the curve.

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a

What are the coordinates of the point at which $g\left(x\right)$g(x) is a tangent to the curve $f\left(x\right)$f(x)?

Note that this point has integer coordinates. Give your answer in the form $\left(a,b\right)$(a,b).

b

What is the gradient of the tangent line?

c

Hence determine the equation of the line $y=g\left(x\right)$y=g(x).

Easy
2min

Consider the curve $f\left(x\right)$f(x) drawn below along with $g\left(x\right)$g(x), which is a tangent to the curve.

Easy
1min

Consider the curve $f\left(x\right)$f(x) drawn below along with $g\left(x\right)$g(x), which is a tangent to the curve.

Easy
1min

Consider the curve $f\left(x\right)$f(x) drawn below along with $g\left(x\right)$g(x), which is a tangent to the curve.

Easy
< 1min
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Outcomes

ACMMM085

interpret the derivative as the slope or gradient of a tangent line of the graph of y=f(x)

ACMMM093

find the slope of a tangent and the equation of the tangent

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