Analyzing the given condition for a twice differentiable function $(f(0))^2 + (f'(0))^2 = 85$.
112648
For every twice differentiable function $f : \bf R \rightarrow [–2, 2]$ with $(f(0))^2 + (f'(0))^2 = 85$, which of the following statements are TRUE?
109896
Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
149764
If $f$ s twice differentiable and satisfies the following constraints, prove $f'(0)>-\sqrt 2$
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 $\mathbb R$
139216
Use the definition of derivative to find $f'(x)$ for $f(x) = x^{1/2}$.
38923
What can we say about differentiability of $f$ at $c$?
137527
if $f(x)$ is differentiable at a x, prove that: $\lim_{h\to0}\frac{f(x+h)-f(x-h)}{2h}$
43956
Differentiating $f(x)^{g(x)}$
144859
Finding parameters for $f(x) = x^2 + 2(m − a)x + 3am −2 = 0$ that satisfy a condition.
74100
How do you solve $f'(x) = f(f(x))$?
111458
Prove that $f$ is differentiable
61486
Show that $f$ is not differentiable at $(0,0)$ - $\frac{x_1^2x_2}{x_1^2+x_2^2}$
105084
Let f be a function twice differentiable and with derivatives continuous on an interval $[a,b]$ containing $0$. Prove the following statement:
107894
Inequality involving the sup of a function and its first and second derivatives
117338
Counterexample to second derivative test when f''(x) is not continuously differentiable
30533
Showing that this function is infinitely differentiable