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

Differentiability: Level 3 Challenges

$\large{x^3+x^2-5x-1=0}$

Let $\alpha,\beta,\gamma$ be the roots of the equation above.

Evaluate $\left\lfloor \alpha \right\rfloor +\left\lfloor \beta \right\rfloor +\left\lfloor \gamma \right\rfloor$ .

Image Credit: Wikimedia N.Mori.

Show explanation

View wiki

by Tanishq Varshney

Are you sure you want to view the solution?

Cancel Yes I'm sure

Let $f$ be a twice differentiable function satisfying $f(1)=1, f(2)=4, f(3)=9$ , then :

f''(x)=2 \forall x \in \mathbb{R}

There exists at least one

x \in (1,3)

such that

f''(x)=2

. None of the given is true.

f'(x)=5 \forall x \in \mathbb{R}

Show explanation

View wiki

by Sandeep Bhardwaj

Are you sure you want to view the solution?

Cancel Yes I'm sure

Let $0<a<b<\frac { \pi }{ 2 }$ . If $f\left( x \right) =\left| \begin{matrix} \sin { x } & \sin { a } & \sin { b } \\ \cos { x } & \cos { a } & \cos { b } \\ \tan { x } & \tan { a } & \tan { b } \end{matrix} \right|$ , then minimum possible number of roots of $f'\left( x \right) =0$ lying in $(a,b)$ is: