Maximum and Minimum Turning Points (Leaving Cert Mathematics): Quizzes

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Maximum and Minimum Turning Points
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What is the key condition that must be true at any turning point of a curve?

dydx=0\frac{dy}{dx} = 0

What is the nature of the tangent line to a curve at a turning point?

Horizontal (parallel to x-axis)

If turning points are at (2,8)(2, 8) and (5,−3)(5, -3), which is the maximum?

(2,8)(2, 8)

What does the second derivative test tell us if d2ydx2<0\frac{d^2y}{dx^2} < 0 at a turning point?

It is a maximum

What does the second derivative test tell us if d2ydx2>0\frac{d^2y}{dx^2} > 0 at a turning point?

It is a minimum

For the quadratic y=3x2−6x+1y = 3x^2 - 6x + 1, what type of turning point does it have?

Minimum

For the quadratic y=−2x2+5x−1y = -2x^2 + 5x - 1, what type of turning point does it have?

Maximum

When is a function increasing?

When dydx>0\frac{dy}{dx} > 0

When is a function decreasing?

When dydx<0\frac{dy}{dx} < 0

What is the first step in finding turning points of a function?

Find first derivative dydx\frac{dy}{dx}

How many turning points does a quadratic function y=ax2+bx+cy = ax^2 + bx + c have?

Exactly one

After finding xx-values where dydx=0\frac{dy}{dx} = 0, what is the next step?

Substitute into original function

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