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?

# MA005 Calculus HELP NEEDED

**student**#1

**student**#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?

**sachin_t**#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 .