There are two lines through the point (-1,5) that are tangent to the parabola f(x)=x^2-2x. Find...
There are two lines through the point (-1,5) that are tangent to
the parabola
f(x)=x^2-2x. Find the x-coordinates of the points where these lines
touch the parabola.
Homework Answers
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There are two lines through the point (-1,5) that are tangent to
the parabola
f(x)=x^2-2x. Find...
Below is a Mathematica graph of the parabola y =- - +6. On the graph, sketch...
Below is a Mathematica graph of the parabola y =- - +6. On the graph, sketch by hand the two tangent lines to the parabola that pass through the point (0,8). Now find the exact coordinates of the two points where these tangent lines touch the parabola.
Let f(x) = x². There are two lines with positive slope that are tangent to the...
Let f(x) = x². There are two lines with positive slope that are tangent to the parabola and that pass through the point (5, 22.75). Find the equation of the line with the smaller slope.
Consider the quadratic function: f(x)=2x^2−8x+2 . Find the following for this parabola. A) The line of...
Consider the quadratic function: f(x)=2x^2−8x+2 . Find the following for this parabola. A) The line of symmetry: B) The vertex: C) The vertical intercept is the point D) Give the coordinates of the two xx intercepts of the parabola as ordered pairs.
Consider the parabola y = 7x - x2. Find the slope m of the tangent line to the parabola at the point (1, 6). using t...
Consider the parabola y = 7x - x2. Find the slope m of the tangent line to the parabola at the point (1, 6). using this definition: The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope m=lim x rightarrow a f(x)-f(a)/x-a provided that this limit exists. m = using this equation: m=lim h rightarrow 0 f(a+h)-f(a)/h m= Find an equation of the tangent line in part (a). y...
Graph the function f(x) = -2, and draw the tangent lines to the graph at points...
Graph the function f(x) = -2, and draw the tangent lines to the graph at points whose x-coordinates are -2,0, and Clear All Draw: F f(x+h)-f(x) Find the difference quotient Preview Find f'(x) by determining lim f(a+h)-f(x) h Preview
The tangent line to the graph of f(x) at x 1 is shown. On the tangent...
The tangent line to the graph of f(x) at x 1 is shown. On the tangent line, P is the point of tangency and A is another point on the line. A y f(x) X -2 2 3 -2 -3 (a) Find the coordinates of the points P and A P(x, y) A(x, y) (b) Use the coordinates of P and A to find the slope of the tangent line (c) Find f'(1) (d) Find the instantaneous rate of change...
6. For a certain function f(x) we have: f'(x) = (x - 3)²(2x - 3) and...
6. For a certain function f(x) we have: f'(x) = (x - 3)²(2x - 3) and • f"(x) = 6(x - 3)(x - 2) (a) Use f' to find the intervals where f is increasing, the intervals where f is decreasing, the x- coordinates and nature (max, min or neither) of any local extreme values. (b) Use f" to find the intervals where the graph of f is concave up, the intervals where the graph of f is concave down...
Let f(x) = z² and g(x) = (1 - 5)² + 10. There is one line...
Let f(x) = z² and g(x) = (1 - 5)² + 10. There is one line with positive slope that is tangent to both of the parabolas y = f(x) and y = g(x) simultaneously. ye9bx)/ y=f/ Find the equation of the line. y= On a separate piece of paper, sketch the graph of the parabola y = 2? + 6. On the same graph, plot the point(0, – 3). Note that there are two tangent lines of y =...
2. Find the equation of the tangent line to f(x)=- V13 - 3x at the point...
2. Find the equation of the tangent line to f(x)=- V13 - 3x at the point x = -3. Express slope and coordinates using exact (radical) form or if using decimal fractions round to at least 3 decimal places. You may leave your equation in point-slope form to save time. (4 points)
Find the slope of the line tangent to f(x) at x = 3. The graph of...
Find the slope of the line tangent to f(x) at x = 3. The graph of f(x) is shown below. Move the point on the curve to x = 3. Then plot two points on the tangent line. Finally, calculate the slope of the tangent line at x = 3. Answer 2 Points Keypad Points can be moved by dragging or using the arrow keys. Any lines or curves will be drawn once all required points are plotted and will...
Below is a Mathematica graph of the parabola y =- - +6. On the graph, sketch by hand the two tangent lines to the parabola that pass through the point (0,8). Now find the exact coordinates of the two points where these tangent lines touch the parabola.
Let f(x) = x². There are two lines with positive slope that are tangent to the parabola and that pass through the point (5, 22.75). Find the equation of the line with the smaller slope.
Consider the parabola y = 7x - x2. Find the slope m of the tangent line to the parabola at the point (1, 6). using this definition: The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope m=lim x rightarrow a f(x)-f(a)/x-a provided that this limit exists. m = using this equation: m=lim h rightarrow 0 f(a+h)-f(a)/h m= Find an equation of the tangent line in part (a). y...
Graph the function f(x) = -2, and draw the tangent lines to the graph at points whose x-coordinates are -2,0, and Clear All Draw: F f(x+h)-f(x) Find the difference quotient Preview Find f'(x) by determining lim f(a+h)-f(x) h Preview
The tangent line to the graph of f(x) at x 1 is shown. On the tangent line, P is the point of tangency and A is another point on the line. A y f(x) X -2 2 3 -2 -3 (a) Find the coordinates of the points P and A P(x, y) A(x, y) (b) Use the coordinates of P and A to find the slope of the tangent line (c) Find f'(1) (d) Find the instantaneous rate of change...
6. For a certain function f(x) we have: f'(x) = (x - 3)²(2x - 3) and • f"(x) = 6(x - 3)(x - 2) (a) Use f' to find the intervals where f is increasing, the intervals where f is decreasing, the x- coordinates and nature (max, min or neither) of any local extreme values. (b) Use f" to find the intervals where the graph of f is concave up, the intervals where the graph of f is concave down...
Let f(x) = z² and g(x) = (1 - 5)² + 10. There is one line with positive slope that is tangent to both of the parabolas y = f(x) and y = g(x) simultaneously. ye9bx)/ y=f/ Find the equation of the line. y= On a separate piece of paper, sketch the graph of the parabola y = 2? + 6. On the same graph, plot the point(0, – 3). Note that there are two tangent lines of y =...
2. Find the equation of the tangent line to f(x)=- V13 - 3x at the point x = -3. Express slope and coordinates using exact (radical) form or if using decimal fractions round to at least 3 decimal places. You may leave your equation in point-slope form to save time. (4 points)
Find the slope of the line tangent to f(x) at x = 3. The graph of f(x) is shown below. Move the point on the curve to x = 3. Then plot two points on the tangent line. Finally, calculate the slope of the tangent line at x = 3. Answer 2 Points Keypad Points can be moved by dragging or using the arrow keys. Any lines or curves will be drawn once all required points are plotted and will...
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