Applications of Differentiation II Lowersixth Science Mathematics

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Test your understanding of graphs, rates, and inflection.

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Applications of Differentiation II Lowersixth Science Mathematics


Applications of Differentiation II Lowersixth Science MathematicsOnline version Test your understanding of graphs, rates, and inflection. by YAKILI LMS 1 The graph of a function can be used to estimate solutions to equations graphically by intersection with y=0. Yes No 2 Polynomial graphs can have 0, 1, 2, or more turning points depending on degree. Yes No 3 For f(x)=x^4, the graph has a horizontal tangent at every point. Yes No 4 A cubic polynomial can have four turning points. Yes No 5 The second derivative test helps identify inflection points by sign change. Yes No 6 A function's rate of change can be approximated using difference quotients. Yes No 7 The second derivative is always positive for inflection points. Yes No 8 A function's average rate of change equals f'(c) for some c in the interval. Yes No 9 The graph of y=\|x\| has more than one inflection point. Yes No 10 The graph of y=x^3 has an inflection point at x=0. Yes No 11 An inflection point occurs where f''(x)=0 or undefined and changes sign. Yes No 12 The end behavior of x^3 is to go to negative infinity on the left and positive infinity on the right. Yes No 13 The slope of a tangent is always equal to the average rate of change over any interval. Yes No 14 The second derivative test can identify inflection points without sign change. Yes No 15 The rate of change at a point is the instantaneous slope. Yes No 16 The equation f(x)=0 can be solved by graphing f(x) and horizontal line y=1. Yes No 17 An inflection point is a point on a curve where concavity changes. Yes No 18 If a point on a graph satisfies f(x)=0, it is a root of the equation. Yes No 19 A quadratic function's graph is a parabola. Yes No 20 The graph of y=\|x\| is differentiable at x=0. Yes No 21 For small changes Δx, Δy equals f(x)Δx. Yes No 22 The derivative of x^3 is a constant. Yes No 23 A polynomial of degree n has exactly n turning points. Yes No 24 A graph can show the point of intersection between two functions solving equations like f(x)=g(x). Yes No 25 The end behavior of a polynomial is independent of the leading coefficient. Yes No 26 The graph of y=sin(x) is a polynomial. Yes No 27 The slope of the tangent line at a point equals f'(x). Yes No 28 An inflection point is always a local maximum. Yes No 29 A graph can show where a function increases or decreases by the sign of derivative. Yes No 30 A small percentage increment can be approximated by multiplying by (1+percentage). Yes No 31 The sum of roots of a polynomial equals the constant term. Yes No 32 The graph of a linear function can have more than one turning point. Yes No 33 The graph of y=x^2 has an inflection point at x=0. Yes No 34 For small changes Δx, Δy ≈ f'(x)Δx. Yes No 35 The average rate of change over an interval equals [f(b)-f(a)]/(b-a). Yes No 36 The turning points of a polynomial are always where the function value is zero. Yes No 37 A polynomial of even degree has the same end behavior at both ends. Yes No 38 The graph of y=f(x) can be used to solve f(x)=k by finding x where y=k. Yes No 39 For a polynomial, the end behavior is determined by the leading term. Yes No 40 The derivative of a polynomial is not defined anywhere. Yes No 41 The sign of f''(x) alone determines increasing/decreasing of f. Yes No 42 The graph of a constant function is a horizontal line with nonzero slope. Yes No 43 A true inflection point does not necessarily correspond to a local maximum or minimum. Yes No 44 The derivative gives the slope of the tangent to a curve. Yes No 45 The derivative of a quadratic is constant. Yes No 46 The graph of a cubic polynomial can have up to two turning points. Yes No 47 A function with a local maximum must have a root between the endpoints of an interval where it is positive. Yes No 48 The derivative of a polynomial is also a polynomial. Yes No 49 For polynomial graphs, the x-intercepts indicate approximate real roots of equations. Yes No 50 An inflection point is where the curve changes concavity. Yes No

Applications of Differentiation II Lowersixth Science Mathematics

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Applications of Differentiation II Lowersixth Science MathematicsOnline version

by YAKILI LMS

The graph of a function can be used to estimate solutions to equations graphically by intersection with y=0.

Polynomial graphs can have 0, 1, 2, or more turning points depending on degree.

For f(x)=x^4, the graph has a horizontal tangent at every point.

A cubic polynomial can have four turning points.

The second derivative test helps identify inflection points by sign change.

A function's rate of change can be approximated using difference quotients.

The second derivative is always positive for inflection points.

A function's average rate of change equals f'(c) for some c in the interval.

The graph of y=|x| has more than one inflection point.

The graph of y=x^3 has an inflection point at x=0.

An inflection point occurs where f''(x)=0 or undefined and changes sign.

The end behavior of x^3 is to go to negative infinity on the left and positive infinity on the right.

The slope of a tangent is always equal to the average rate of change over any interval.

The second derivative test can identify inflection points without sign change.

The rate of change at a point is the instantaneous slope.

The equation f(x)=0 can be solved by graphing f(x) and horizontal line y=1.

An inflection point is a point on a curve where concavity changes.

If a point on a graph satisfies f(x)=0, it is a root of the equation.

A quadratic function's graph is a parabola.

The graph of y=|x| is differentiable at x=0.

For small changes Δx, Δy equals f(x)Δx.

The derivative of x^3 is a constant.

A polynomial of degree n has exactly n turning points.

A graph can show the point of intersection between two functions solving equations like f(x)=g(x).

The end behavior of a polynomial is independent of the leading coefficient.

The graph of y=sin(x) is a polynomial.

The slope of the tangent line at a point equals f'(x).

An inflection point is always a local maximum.

A graph can show where a function increases or decreases by the sign of derivative.

A small percentage increment can be approximated by multiplying by (1+percentage).

The sum of roots of a polynomial equals the constant term.

The graph of a linear function can have more than one turning point.

The graph of y=x^2 has an inflection point at x=0.

For small changes Δx, Δy ≈ f'(x)Δx.

The average rate of change over an interval equals [f(b)-f(a)]/(b-a).

The turning points of a polynomial are always where the function value is zero.

A polynomial of even degree has the same end behavior at both ends.

The graph of y=f(x) can be used to solve f(x)=k by finding x where y=k.

For a polynomial, the end behavior is determined by the leading term.

The derivative of a polynomial is not defined anywhere.

The sign of f''(x) alone determines increasing/decreasing of f.

The graph of a constant function is a horizontal line with nonzero slope.

A true inflection point does not necessarily correspond to a local maximum or minimum.

The derivative gives the slope of the tangent to a curve.

The derivative of a quadratic is constant.

The graph of a cubic polynomial can have up to two turning points.

A function with a local maximum must have a root between the endpoints of an interval where it is positive.

The derivative of a polynomial is also a polynomial.

For polynomial graphs, the x-intercepts indicate approximate real roots of equations.

An inflection point is where the curve changes concavity.