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

Step 1: Slope is given by Step 2
Let us assume that the engine is turned off at the point on the curve .
As per given condition must have go to the tangent line to the curve at point .
The point is on the curve , so The point will be .
Slope of the tangent line is given by, Step 3:
Equation of the tangent line at is given by Equation of the tangent line at is Step 4:
Equation of the tangent line at is Equation of the tangent line at is The value of are not real, so no real point is exist which passed through point .
Conclusion:
There is no any point exist such that the engine turned off in order to coast along the tangent line at point .

#5

Thank you! Now I understand.