(a) Find the slope m of the tangent to the curve y = 2 + 4x2 − 2x3 at the point where x = a. m = (b) Find equations of the tangent lines at the points (1, 4) and (2, 2). y(x) = (at the point (1, 4)) y(x) = (at the point (2, 2)) (c) Graph the curve and both tangents on a common screen. say and the sose m of the target to the survey * 2...
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.
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 =...
Find an equation of the tangent line to the graph of the function at the given point. 1 s(x) = x² - 2x + 16' (2, 1) y = Use a graphing utility to graph the function and the tangent line in the same viewing window. y y 1.0 1.04 0.5 0.5 10 5 10 -0.51 -0.5
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...
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...
(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 of a level curve of the function f(x, y) = 2e2 y? (6 marks) (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 of a level curve of the function f(x, y) = 2e2 y? (6 marks)
f(a+h)-f(a) a. Use the definition mun lim to find the slope of the line tangent to the graph off at P. h-+0 h b. Determine an equation of the tangent line at P. f(x)-3x+7, P(2.1) a. man b.y=0 19
please help Find the function f given that the slope of the tangent line to the graph off at any point (x, f(x)) is f(x appropriate.) f'(x) = et + 7x; (0,9) f(x) = et + x +8 Submit Answer View Previous Question Question Home My Assignments Math problem 15.jpg Math Problem 14.jpg Type here to search o e a Find the function folven that the slope of the tangent line to the graph of Fat My point (x,x) is...
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...