If $f$ is thrice differentiable on $[−1,1]$ such that $f(−1)=0,f(1)=1$ and $f'(0)=0$, then $f'''(c)\ge3$ for some $c\in(−1,1)$.
101371
show that $f^{(3)}(c) \ge 3$ for $c\in(-1,1)$
105068
Proving that the function is differentiable and $f'(0)=0$
138864
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f(x+y)=f(x)f(y)$ and $f'(0)$ exists, then $f$ is differentiable on $\mathbb R$
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
130322
Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
96450
If $f(x)$ is continuous and differentiable function , prove that $f(x) \geq e^{3x}, \forall x \geq 0$
17310
Can $f(x)=|x|^3$ be differentiated
94193
determine whether $f(x, y) = \frac{xy^3}{x^2 + y^4}$ is differentiable at $(0, 0)$.
13150
If the derivative of $f$ is never zero, then $f$ is one-to-one
129324
Let $f:[0;1]\to\mathbb R$ be continiously differentiable
57193
Prove that $f$ has derivatives of all orders at $x=0$, and that $f^{(n)}(0)=0$ for $n=1,2,3\ldots$
43956
Differentiating $f(x)^{g(x)}$
38923
What can we say about differentiability of $f$ at $c$?
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
111470
Proof of differentiability of $f(x)$
148737
Is $|xy|$ differentiable in $(0,0)$?