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Calculus

Differentiability

Concept Quizzes

Approximate Rate of Change
Slope of a Curve
Tangent Line at a Point
Local Linear Approximation
Intermediate Value Theorem
Mean Value Theorem
Rolle's Theorem
Characteristics of graphs of f and f'

Challenge Quizzes

Differentiability: Level 2 Challenges
Differentiability: Level 3 Challenges
Differentiability: Level 4 Challenges

Approximate Rate of Change

What is the average rate of change of the function $f(x)=6x^2+px+q$ on the interval $[a,b] ?$

a+b+p+q

a+b+p

6a+6b+p

36a+36b+p

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by Brilliant Staff

Given the symmetric difference quotient, $f'(a) \approx \frac{f(a+h)-f(a-h)}{2h},$ approximate $f'(2)$ using the symmetric difference quotient for the function $f(x)=x^4$ with $h=0.04.$

32.013 32.026 32.051 32.006

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by Brilliant Staff

What is the average rate of change of the function $y=2x^2+7$ when the value of $x$ changes from $5$ to $7?$

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by Brilliant Staff

What is the slope of the secant line that passes through the two points $(x,f(x))$ on the graph of the function $f(x)=x^2,$ for $x=2$ and $x=2.004?$

4.004 2.004 3.996 1.996

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by Brilliant Staff

If $f(x)=-7x+3,$ what is the average rate of change of $f(x)$ when $x$ changes from $4$ to $7?$

-4 -11 -7 7

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by Brilliant Staff

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