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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

Intermediate Value Theorem

Between which of the following two values does the equation $-5x^4 + 7x^2 + 1=0$ have a solution?

\text{Between } -1 \text{ and } 0.

\text{Between } -3 \text{ and } -2.

\text{Between } 0 \text{ and } 1.

\text{Between } -2 \text{ and } -1.

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by Brilliant Staff

Between which of the following two values does the equation $4x^3 + 7x - 13=0$ have a solution?

\text{Between } 0 \text{ and } 1.

\text{Between } -2 \text{ and } -1.

\text{Between } -1 \text{ and } 0.

\text{Between } 1 \text{ and } 2.

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by Brilliant Staff

For the function $f(x)=2x,$ which of the following lies in the range of $f$ in the interval $[0, 1]?$

1 5 -1 -3

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by Brilliant Staff

$f(x)$ is a continuous function on the interval $[25, 40]$ . If $f(25) = 51$ , $f(40) = 13$ , and $f(a) = - 56$ where $25 < a < 40$ , what are the least number of solutions to $f(x) = 0$ ?

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Given the function $\displaystyle{f(x)=\frac{24x+8}{5x^2 - 15}},$ how many solutions does the equation $f(x)=0$ have on the domain $[-2, 2]?$

2 1 3 0

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by Brilliant Staff

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