Tangents and Curves (Leaving Cert Mathematics): Quizzes

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Tangents and Curves
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What does dydx\frac{dy}{dx} represent for a curve?

The slope of the tangent at any point

A tangent to a curve touches the curve at how many points?

Exactly one point

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

Find dydx\frac{dy}{dx} by differentiating

What is the point-slope form used for finding tangent equations?

y−y1=m(x−x1)y - y_1 = m(x - x_1)

In the formula y−y1=m(x−x1)y - y_1 = m(x - x_1), what does mm represent?

The slope of the tangent

What is the relationship between the slopes of parallel lines?

They are equal

What do the slopes of perpendicular lines multiply to give?

-1

For y=3x2+4x−5y = 3x^2 + 4x - 5, what is dydx\frac{dy}{dx}?

6x+46x + 4

For y=3x2+4x−5y = 3x^2 + 4x - 5, what is the slope of the tangent at x=1x = 1?

10

When finding coordinates with a given slope, what should you do with dydx\frac{dy}{dx}?

Set it equal to that slope

To find a tangent parallel to y=3x+4y = 3x + 4, what must the tangent's slope be?

3

What is the three-step method for finding tangent equations?

Differentiate, substitute, point-slope

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