Last updated on Oct 23, 2026

The Slope of a Curve (Leaving Cert Mathematics): Quizzes

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The Slope of a Curve

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What is the slope of a curve at any point?

The slope of the tangent line there

What is a tangent line to a curve?

Line touching at one point, same slope

If $y = x^5$ , what is $\frac{dy}{dx}$ ?

$5x^4$

What is the derivative of a constant such as 7?

$0$

If $y = 4x$ , what is $\frac{dy}{dx}$ ?

$4$

If $y = x^3 + 2x^2$ , what is $\frac{dy}{dx}$ ?

$3x^2 + 4x$

If $f(x) = x^2 - 4x$ , what is $f'(3)$ ?

$2$

What does $f'(x)$ represent?

Same as $\frac{dy}{dx}$

For $y = x^2$ , what is $\frac{dy}{dx}$ ?

$2x$

For curve $y = x^2$ at $x = 2$ , what is the slope?

$4$

What does $\frac{dy}{dx}$ tell us?

Slope at any x-value

In the power rule, after multiplying by the power, what must you do?

Reduce the power by 1

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