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On a separate piece of paper, sketch the graph of the parabola y= +4. On the same graph, plot the point(0, -3). Note that there are two tangent lines of y = z² + 4 that pass through the point (0, -3). W Specifically, the tangent line of the parabola y ==?+ 4 at the point (a, a? + 1) passes through the point (0, -3) where a > 0. The other tangent line that passes through the point(0, -3)...
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...
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.
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...
Let f(x) = 2 + 5x2 – 2x3. (a) Find the slope m of the tangent line to the graph off at the point where x = a. ma (b) Find an equation of the tangent line to the graph off at the point (1, 5). y(x) = (c) Find an equation of the tangent line to the graph off at the point (2,6). y(x) = (d) Use technology to graph fand the two tangent lines in the same viewing...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
2:45 webassign.net ASSnts A LCal 0 Consider the function f(x) and the point P(4,2) on the graph f (a) Graph fand the secant lines passing through the point P(4, 2) and Q(x, fx)) for x-values of 1, 6, and 8 (b) Find the slope of each secant line. (Round your answers to three decimal places.) (line passing through Q(1, f(x)) (line passing through Q(6, fx)) (line passing through Q(8, f(x)) (c) Use the results of part (b) to estimate the...
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...
Question 4 g A-2 B 6 0 The sketch shows a circle, a parabola, which is the graph of f, and a straight line, which is the graph of g. The parabola has x-intercepts –2 and 6, and y-intercept 6. Its turning point is C. The circle has its centre at the origin and it passes through the point A, which has coordinates (-2,0). At point B both the circle and the straight line cut the x-axis. The straight line...