9000064102
Level:
B
Find the tangent to the graph of the function
\(f(x) = \frac{x+1}
{x-1}\) at the
point \([2;3]\).
\(2x + y - 7 = 0\)
\(2x - y - 1 = 0\)
\(- 2x + y + 1 = 0\)
\(x + 2y - 9 = 0\)
Applications of derivatives
9000064103
Level:
B
Find the normal line to the graph of the function
\(f(x) = 2x^{2} - 2x + 1\) at the
point \([2;5]\).
\(x + 6y - 32 = 0\)
\(6x - y - 7 = 0\)
\(x + 6y - 4 = 0\)
\(- 6x + y - 7 = 0\)
9000064104
Level:
B
Let \(p\) be the tangent to
the graph of the function \(f(x) = x^{2} - x - 6\)
parallel to the line \(y = 3x + 1\).
Find the point \(A\)
where \(p\) touches
the graph of \(f\).
\(A = \left [2;-4\right ]\)
\(A = \left [2;4\right ]\)
\(A = \left [1;6\right ]\)
\(A = \left [-1;-4\right ]\)
9000064105
Level:
B
Find the tangent to the graph of the function
\(f(x) = x\sin x\) at the
point \(\left [ \frac{\pi }{2}; \frac{\pi } {2}\right ]\).
\(y = x\)
\(y = x + 1\)
\(y = 0\)
\(y =\pi -x\)
9000064106
Level:
B
Let \(p\) be the tangent to
the graph of the function \(f(x) = x^{2} + 4x - 2\)
perpendicular to the line \(x + 6y + 2 = 0\).
Find the point \(A\) where
\(p\) touches the graph
of the function \(f\).
\(A = \left [1;3\right ]\)
\(A = \left [-5;3\right ]\)
\(A = \left [-3;-5\right ]\)
\(A = \left [0;-2\right ]\)
9000064107
Level:
B
Find the tangent to the graph of the function
\(f(x) = x^{2} + 4x - 2\) parallel to
the line \(2x + y + 1 = 0\).
\(2x + y + 11 = 0\)
\(2x - y - 1 = 0\)
\(2x + y - 1 = 0\)
\(2x - y - 11 = 0\)
9000064108
Level:
B
Find the normal line to the graph of the function
\(f(x) = 2x^{2} - 7x\) parallel to
the line \(y = -x\).
\(x + y + 4 = 0\)
\(- x + y + 4 = 0\)
\(x - y - 8 = 0\)
\(x + y - 8 = 0\)
9000064109
Level:
B
Find the tangent to the graph of the function
\(f(x) = 3x^{2} - 8x + 2\) perpendicular
to the line \(x + 4y + 5 = 0\).
\(4x - y - 10 = 0\)
\(-4x + y + 1 = 0\)
\(8x - 2y + 1 = 0\)
\(-8x + 2y - 10 = 0\)
9000064110
Level:
B
Identify a true statement related to the function
\(f(x) = \frac{x-1}
{x+1}\).
The tangent at \(T = [-3;2]\)
is parallel to \(x - 2y + 1 = 0\).
The tangent at \(T = [-3;2]\)
contains the point \(A = \left [1;-4\right ]\).
The slope of the tangent at \(T = [-3;2]\)
is \(2\).
The tangent at \(T = [-3;2]\) is
perpendicular to \(x + 2y + 1 = 0\).
1003263403
Level:
C
Find the global extrema of the following function on the interval \( [0;3] \).
\[ f(x)=2x^3-3x^2-12x \]
the global minimum at \( x=2 \), the global maximum at \( x=0 \)
the global minimum at \( x=2 \), the global maximum at \( x=-1 \)
the global minimum at \( x=0 \), the global maximum at \( x=2 \)
the global minimum at \( x=3 \), the global maximum at \( x=0 \)