MA005 Calculus HELP NEEDED


#1

At what point should the engine be turned off in order to coast along the tangent line to a base at (1,3)?
This doesn’t exist because it is inside the parabola. But, how do I find that out?


#2

Also, how does one find f(x) given f’(x)? This is questions 32-37 in MA005 3.2, but I don’t see how to solve this?


#4

Step 1) Find the slope of image .
Step 2) Consider the points image and find the value of the slope at that point.
Step 3) Find equation of the tangent line using image .
Step 4) Find equation of the tangent at image and solve for image .

Step 1:
image
Slope is given by image

Step 2
Let us assume that the engine is turned off at the point image on the curveimage .
As per given condition image must have go to the tangent line to the curve at point image .
The point image is on the curve image , so image
The point will be image .
Slope of the tangent line is given by,
image

Step 3:
Equation of the tangent line at image is given by
image
Equation of the tangent line at image is image

Step 4:
Equation of the tangent line at image is image
Equation of the tangent line at image is
image
The value of image are not real, so no real point is exist which passed through point image .
Conclusion:
There is no any point exist such that the engine turned off in order to coast along the tangent line at point image .


#5

Thank you! Now I understand.