
(a) For what value(s) of x does the graph of 2x3 2a2 5 f(x) have a horizontal tangent? (6 marks) |(b) What is the slope...
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...
30 6 9 Compute the slope of the line tangent to the 36 Consider the upper half of the ellipsoid f(x,y) = and the point P on the level curve f(x,y) - level curve at P, and verify that the tangent line is orthogonal to the gradient at that point. 245 A. The slope is 5 OB. The slope is undefined, so the tangent line is vertical Verify that the tangent line is orthogonal to the gradient at P Select...
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...
1+1 5. [10 marks) Find all values of k such that f(x) = -r2 + 2kr +1" has domain (-0,0). 6. [10 marks] Sketch the graph of y = -2 -2 log: (2-2) and find its domain, range, -intercept and y-intercept. Show your transformations step by step. 7. (12 marks] (a) [8 marks) Find the equation of the tangent line to the graph of the function f(x) = 3.0" - 6x2 - 7 at = 2 (b) (4 marks) Find...
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...
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) = x² - 10x - 9. a. Find the value(s) of x for which the slope of the curve y = f(x) is 0. b. Find the value(s) of x for which the slope of the curve y = f(x) is - 2. a. The point(s) at which the slope of a tangent line is 0 is (Type an ordered pair. Use a comma to separate answers as needed.) b. The point(s) at which the slope of a...
Consider the function and the value of a. f(x) = -5 X - 1 a = 3 (a) Use mtan f(a+h) - f(a) = lim to find the slope of the tangent line mtan h0 h = f'(a). = mtan 5 4 (b) Find the equation of the tangent line to fat x = a. (Let x be the independent variable and y be the dependent variable.) »- 3 = (x – 3) x Consider the graph. у 5 x...
3. For what value(s) of x in the interval [0, 21) is the tangent line to the graph of the function f(x) = 2 cos x is parallel to the line y= V3x + 5?
Begin by graphing the absolute value function, f(x)= |x|. Then use transformations of this graph to graph the given function. g(x)-3 x-2| +4 What transformations are needed order to obtain the graph of g(x) from the graph of f(x)? Select all that apply. A. Vertical shift B. Reflection about the y-axis C. Vertical stretch/shrink D. Horizontal shift E. Reflection about the x-axis F. Horizontal stretch/shrink Choose the correct graph below. O C. O D. O A. ОВ. A V 40...