TEST 33
1.
\(f(x)=\begin{cases}x^2-1&x\ge1\\6x+2&x<1\end{cases}\)
\(\Rightarrow f'(2)+f'(-1)=?\)
A) \(16\)B) \(10\)C) \(8\)D) \(4\)E) \(2\)
2.
\(f(x)=\begin{cases}3x^2-1&x\ge2\\x^2+4x&x<2\end{cases}\)
\(\Rightarrow f'(2^-)+f'(2^+)=?\)
A) \(20\)B) \(18\)C) \(16\)D) \(12\)E) \(8\)
3.
\(f(x)=\begin{cases}x^3+1&x>1\\2&x=1\\3x-1&x<1\end{cases}\)
\(\Rightarrow f'(1)=?\)
A) \(0\)B) \(1\)C) \(2\)D) \(3\)E) \(\varnothing\)
4.
\(f(x)=\begin{cases}2x-1&x<3\\x^2-4x+8&x\ge3\end{cases}\)
\(\Rightarrow f'(3)=?\)
A) \(0\)B) \(1\)C) \(2\)D) \(8\)E) \(\varnothing\)
5.
\(f(x)=\begin{cases}\ln(x+3)&x\ge-2\\x+2&x<-2\end{cases}\)
\(\Rightarrow f'(-2)=?\)
A) \(0\)B) \(1\)C) \(2\)D) \(3\)E) \(\varnothing\)
6.
\(k\in\mathbb R\)
\(f(x)=\begin{cases}ax-bx^2&x\ge1\\2x^3-1&x<1\end{cases}\)
\(f'(1)=k\)
\(\Rightarrow b=?\)
A) \(-5\)B) \(-4\)C) \(-2\)D) \(1\)E) \(2\)
7.
\(f(x)=\begin{cases}x^2-1&x\ge2\\x+2&x<2\end{cases}\)
\(\Rightarrow f'(1)+f'(3)=?\)
A) \(8\)B) \(7\)C) \(6\)D) \(5\)E) \(4\)
8.
\(f(x)=\begin{cases}x^3+2x&x>1\\x^2-4x&x\le1\end{cases}\)
\(\Rightarrow f'(3)+2\cdot f'(-1)=?\)
A) \(17\)B) \(15\)C) \(13\)D) \(12\)E) \(9\)