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iGCSE (2021 Edition)

26.04 Equations of tangents (Extended)

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

0580E2.13A

Understand the idea of a derived function. Use the derivatives of functions of the form ax^n, and simple sums of not more than three of these.

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