Applications of Differention Lowersixth Science Mathematics

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Key concepts on derivatives and concavity.

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Applications of Differention Lowersixth Science Mathematics


Froggy Jumps Applications of Differention Lowersixth Science MathematicsOnline version Key concepts on derivatives and concavity. by YAKILI LMS 1 What indicates a turning point on a function f(x) with f'(x)=0? a A local maximum or minimum b An inflection point c A global maximum 2 If f'(x) changes from positive to negative at x=a, then a is: a A point of inflection b A local maximum c A local minimum 3 If f'(x) changes from negative to positive at x=a, then a is: a A local minimum b A local maximum c An asymptote 4 First derivative test is used to determine: a Second derivative values b Increasing/decreasing intervals and turning points c Concavity only 5 Second derivative f''(x) > 0 implies the function is: a Convex (concave up) b Linear c Concave down 6 If f''(x) < 0, the function is: a Concave up b Linear c Concave down 7 If f''(a)=0, the second derivative test is: a Always a min b Always a max c Inconclusive 8 An inflection point occurs where the function: a Changes concavity b is discontinuous c has a derivative zero 9 A function increasing on an interval means f'(x): a Is positive on that interval b Is negative c Is zero 10 A function decreasing on an interval means f'(x): a Is negative on that interval b Is positive c Is zero 11 If f'(x) is increasing, then f''(x) is: a Zero b Negative c Positive 12 A critical point occurs when: a f''(x)=0 b f(x)=0 c f'(x)=0 or f'(x) is undefined 13 The first derivative test helps identify: a Inflection points b Local extrema c Global extrema 14 If f'(x) changes sign from + to -, the point is: a A local minimum b A local maximum c No extremum 15 If f'(x) changes sign from - to +, the point is: a A local minimum b A saddle point c A local maximum 16 Which test uses f''(x) to classify extrema? a Second derivative test b First derivative test c Concavity test 17 On an interval where f''(x)>0, f is: a Concave down b Linear c Convex (concave up) 18 On an interval where f''(x)<0, f is: a Convex (concave up) b Linear c Concave down 19 If a point is an inflection point, then: a Concavity changes b Function is discontinuous c Derivative is zero 20 What does the monotonicity of f help determine? a Where it has zeros b Where the function increases or decreases c Where it is continuous 21 A stationary point is where: a f(x)=0 b f''(x)=0 c f'(x)=0 22 Turning point is another term for: a Local extremum b Asymptote c Inflection point 23 Which test requires f''(x) to be computed? a First derivative test b Second derivative test c Monotonicity test 24 If f' is zero at x=a and f''(a)<0, then a is: a Local minimum b Inflection point c Local maximum 25 If f' is zero at x=a and f''(a)>0, then a is: a No extremum b Local minimum c Local maximum 26 A function is increasing where f' is: a Positive b Negative c Zero 27 A function is decreasing where f' is: a Zero b Positive c Negative 28 An inflection point occurs when f''(x) crosses: a Zero or undefined b One c Infinity 29 The first derivative test helps locate: a Critical and turning points b Inflection points only c Zeros of f 30 If f''(x) is never zero and always positive, f is: a Linear b Concave down everywhere c Convex up everywhere 31 If f''(x) is never zero and always negative, f is: a Convex up everywhere b Concave down everywhere c Not defined 32 Which test can fail to classify a point if f''=0? a Monotonicity test b First derivative test c Second derivative test 33 A point where f'(x)=0 and f''(x)=0 may require: a Immediate classification b Higher-order test c No test needed 34 If f is increasing and concave up, the slope is: a Constant b Increasing c Decreasing 35 If f is decreasing and concave down, the slope is: a Increasing b Decreasing c Constant 36 A stationary point is classified by: a Sign of f'' only b Sign of f' around the point c Value of f 37 An extremum that occurs without f' changing sign is: a A cusp b Not a local extremum c A corner 38 If a function has f''(x)>0 on an interval, then f' on that interval is: a Constant b Increasing c Decreasing 39 Which indicates a potential turning point without computation? a f(x)=0 b f''(x)=0 c f'(x)=0 40 Concavity change occurs at: a Asymptote b Inflection point c Critical point 41 A function with f' positive and f'' negative is: a Increasing and concave up b Decreasing and concave up c Increasing but concave down 42 A function with f' negative and f'' positive is: a Decreasing but concave up b Decreasing and concave down c Increasing but concave up 43 Which test helps determine concavity without f' sign? a Monotonicity test b First derivative test c Second derivative test 44 If f''(x0)=0 and changes from + to -, the point is: a Local minimum b Local maximum (potential) c Inflection point 45 If f''(x0)=0 and changes from - to +, the point is: a Local minimum (potential) b Local maximum c Inflection point 46 Increasing function with increasing slope is: a Convex up and rising b Constant c Concave down and rising 47 Decreasing function with decreasing slope is: a Concave up and rising b Constant c Concave down and falling 48 The derivative test can reveal: a Where it has zeros b Where a function moves from increasing to decreasing c Where it is discontinuous 49 A point where f' changes sign from + to - is: a Local maximum b Local minimum c Inflection point 50 A point where f' changes sign from - to + is: a Local maximum b No extremum c Local minimum

Applications of Differention Lowersixth Science Mathematics

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Applications of Differention Lowersixth Science MathematicsOnline version

by YAKILI LMS

What indicates a turning point on a function f(x) with f'(x)=0?

If f'(x) changes from positive to negative at x=a, then a is:

If f'(x) changes from negative to positive at x=a, then a is:

First derivative test is used to determine:

Second derivative f''(x) > 0 implies the function is:

If f''(x) < 0, the function is:

If f''(a)=0, the second derivative test is:

An inflection point occurs where the function:

A function increasing on an interval means f'(x):

A function decreasing on an interval means f'(x):

If f'(x) is increasing, then f''(x) is:

A critical point occurs when:

The first derivative test helps identify:

If f'(x) changes sign from + to -, the point is:

If f'(x) changes sign from - to +, the point is:

Which test uses f''(x) to classify extrema?

On an interval where f''(x)>0, f is:

On an interval where f''(x)<0, f is:

If a point is an inflection point, then:

What does the monotonicity of f help determine?

A stationary point is where:

Turning point is another term for:

Which test requires f''(x) to be computed?

If f' is zero at x=a and f''(a)<0, then a is:

If f' is zero at x=a and f''(a)>0, then a is:

A function is increasing where f' is:

A function is decreasing where f' is:

An inflection point occurs when f''(x) crosses:

The first derivative test helps locate:

If f''(x) is never zero and always positive, f is:

If f''(x) is never zero and always negative, f is:

Which test can fail to classify a point if f''=0?

A point where f'(x)=0 and f''(x)=0 may require:

If f is increasing and concave up, the slope is:

If f is decreasing and concave down, the slope is:

A stationary point is classified by:

An extremum that occurs without f' changing sign is:

If a function has f''(x)>0 on an interval, then f' on that interval is:

Which indicates a potential turning point without computation?

Concavity change occurs at:

A function with f' positive and f'' negative is:

A function with f' negative and f'' positive is:

Which test helps determine concavity without f' sign?

If f''(x0)=0 and changes from + to -, the point is:

If f''(x0)=0 and changes from - to +, the point is:

Increasing function with increasing slope is:

Decreasing function with decreasing slope is:

The derivative test can reveal:

A point where f' changes sign from + to - is:

A point where f' changes sign from - to + is: