Slopes of Tangents (Leaving Cert Mathematics): Quizzes

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Slopes of Tangents
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What formula gives the slope of a tangent at xx?

First derivative of the function

Find the slope of the tangent at x=1/2x=1/2 for f(x)=3x2−2x3f(x)=3x^2-2x^3.

f′(x)=6x−6x2f'(x)=6x-6x^2

What is the equation form for a tangent line?

y−y1=m(x−x1)y-y_1=m(x-x_1)

Using the point and slope, find the tangent line at x=1/2x=1/2.

y−(1/2)=1(x−1/2)y-(1/2)=1(x-1/2)

Simplify y−(1/2)=1(x−1/2)y-(1/2)=1(x-1/2).

y=xy=x

What is the key step after finding slope and point?

Write tangent eq.

How is the derivative used in tangent line problems?

To find slope at a point

If f′(x)=6x−6x2f'(x)=6x-6x^2, what is f′(1)f'(1)?

0

What does a zero slope indicate at a point?

Horizontal tangent

Why substitute xx into f′(x)f'(x)?

To find tangent slope

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