3. What point on the line y = 7 - 3x is closest to the origin? a. Sketch the line carefully and mark the point on the line that you think is closest to the origin. b. Write the distance between the origin and a point (x,y) in the plane. If you don't know, think of a triangle with base x and height y. 8 7 6 c. The point must be on the line, so you can write the...
at the point (2, -3). Give an 4. Find the minimum value of the directional derivative of the function f(x, y)- exact answer. 2.
at the point (2, -3). Give an 4. Find the minimum value of the directional derivative of the function f(x, y)- exact answer. 2.
3. Use the definition of the derivative (i.e. evaluate the appropriate limit) to find the derivative of the function y(x)= 8x - 7 at the point P(4, 5).
Find the distance from the point with position vector y=[ 1,-3]| to the line through the origin parallel to y = [-2,4]. Give your answer rounded to 2 decimal places.
RSS3 points 12. Find the point on the curve y=Vx that is a minimum distance from the point (4,0). Report your answer as an ordered pair in the format (x, y) and round each coordinate to the nearest tenth. 13. Consider all lines in the xy-plane that pass through both the origin and a point (x, y) on the graph of the parabola y = x^2 - x + 16 for (1,8). The figure below shows one such line and...
Find the point P on the line y = 3x that is closest to the point (20,0). What is the least distance between P and (20,0)? The point P on the line y = 3x that is closest to the point (20,0) is (Type an ordered pair.) The least distance between P and (20,0) is approximately (Round to the nearest tenth as needed.)
2. Use the ε - δ definition for the limit to prove that limx→-2 (4x - 3) = -113. Use the limit definition of the derivative to find the derivative of the function f(x) = √(4x + 1)4. Find the equation of the tangent line to the curve ve y = (1 + 2x) 10 at the point (-1,1).
Find the equation to the line tangent to y = 1/(x+3) where x = 2 Use the definition of derivative to find the slope, lim laws, and algebra
(1 point) Use the derivative to find the vertex of the parabola y = -3x2 + 12x - 9. Answer: the vertex has coordinates x = and y =
Find the critical point of the function. Then use the second derivative test to classify the nature of this point, if possible. (If an answer does not exist, enter DNE.) f(x, y) = x2 − 4xy + 2y2 + 4x + 8y + 8 critical point (x, y)= classification ---Select--- :relative maximum, relative minimum ,saddle point, inconclusive ,no critical points Finally, determine the relative extrema of the function. (If an answer does not exist, enter DNE.) relative minimum value= relative...