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8.06 Tangents and normals

Interactive practice questions

Consider the curve given by the function $f\left(x\right)=x^3+5x$f(x)=x3+5x.

a

Find the first derivative of the function, $f'\left(x\right)$f(x).

Enter each line of working as an equation.

b

Which of the following notation represents the gradient of the function $f\left(x\right)$f(x) at the point $\left(2,18\right)$(2,18)?

$f\left(18\right)$f(18)

A

$f'\left(2\right)$f(2)

B

$f'\left(18\right)$f(18)

C

$f\left(2\right)$f(2)

D
c

Using the derivative found in part (a), determine the gradient of the tangent $f'\left(x\right)$f(x), at the point $\left(2,18\right)$(2,18).
Enter each line of working as an equation where $f'\left(2\right)$f(2) is the subject.

Easy
2min

At point $M$M$\left(x,y\right)$(x,y), the equation of the tangent to the curve $y=x^2$y=x2 is given by $y=4x-4$y=4x4.

Easy
2min

At point $M$M$\left(x,y\right)$(x,y), the equation of the tangent to the curve $y=x^3$y=x3 is given by $y=12x-16$y=12x16.

Easy
3min

Consider the parabola $f\left(x\right)=x^2+3x-10$f(x)=x2+3x10.

Easy
4min
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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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