Gradients, Tangents & Normals (Edexcel A-Level Mathematics): Quizzes

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Gradients, Tangents & Normal
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What does a tangent to a curve do at a given point?

Touches the curve only once at that point

The gradient of a curve at a point equals what?

The gradient of its tangent at that point

What is the first step in finding the equation of a tangent?

Find the gradient function dydx\frac{dy}{dx}

For y=x3+6x4y = x^3 + 6x - 4, what is dydx\frac{dy}{dx} when x=1x = 1?

99

For y=x3+6x4y = x^3 + 6x - 4, what is yy when x=1x = 1?

33

How are the gradients of a tangent and normal related?

Normal gradient is negative reciprocal

If a tangent has gradient 1717, what is the gradient of the normal?

117-\frac{1}{17}

For y=4x2+x3y = 4x^2 + x - 3, what is dydx\frac{dy}{dx}?

8x+18x + 1

With point (1,3)(1,3) and m=9m = 9, what is the tangent equation?

y=9x6y = 9x - 6

For f(x)=6x52+4f(x) = 6x^{\frac{5}{2}} + 4, what is f(x)f'(x)?

15x3215x^{\frac{3}{2}}

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