Points of Inflection (Leaving Cert Mathematics): Quizzes

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Points of Inflection
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What is a point of inflection?

Where concavity changes

When a function is concave up, what is true about f′′(x)f''(x)?

f′′(x)>0f''(x)>0

When a function is concave down, what is true about f′′(x)f''(x)?

f′′(x)<0f''(x)<0

What shape does a concave up graph have?

∪\cup

At a point of inflection, what happens to f′′(x)f''(x)?

Crosses zero or becomes undefined

What is the first step to find a point of inflection?

Compute f′′(x)f''(x)

After finding f′′(x)f''(x), what should you do next?

Find where f′′(x)=0f''(x)=0

For y=x3−6x2+5x−11y=x^3-6x^2+5x-11, given d2ydx2=6x−12\frac{d^2y}{dx^2}=6x-12, find xx when d2ydx2=0\frac{d^2y}{dx^2}=0.

x=2x=2

For y=x3−6x2+5x−11y=x^3-6x^2+5x-11, what is the point of inflection?

(2,−17)(2,-17)

If solving f′′(x)=0f''(x)=0 leads to −2=0-2=0, what does this mean?

No point of inflection exists

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Curve Sketching

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The Basics

Curve Sketching

Implicit Differentiation

Rates of Change

Trig/Exponential Functions

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The Basics

Curve Sketching

Implicit Differentiation

Rates of Change

Trig/Exponential Functions

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