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

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

Touches curve only once at that point

The gradient of a curve at a point equals the gradient of what?

Its tangent at that point

What is the first step in finding a tangent equation?

Find 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 does the gradient of a normal relate to the tangent's gradient?

Negative reciprocal of tangent

If tangent gradient is 1717, what is the normal gradient?

117-\frac{1}{17}

What is the tangent to y=x3+6x4y = x^3 + 6x - 4 at x=1x = 1?

y=9x6y = 9x - 6

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

1717

What is ddx(6x52)\frac{d}{dx}(6x^{\frac{5}{2}})?

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

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