Help with Straight Line 3y-x-k=0 & Turning Points

[Run Haridan]

Straight line! help!

Homework Statement

the straight line 3y-x-k=0 is the normal to the curve y=4x³+12x²+9x-1 at point A. The curve has two turning points.

a)find the coordinates of A
b)find the coordinates of the turning points of the curve. then, determine whether the turning points are a maximum or a minimum point.

Homework Equations

so can we use simultaneous equation on this question?
or maybe replace y in the equation

The Attempt at a Solution

please help!

 

[redargon]

using simultaneous equations will find the points where the curves intersect (this may be in one or more places, so is not necessarily the one you're looking for, but it does help).

What does normal mean and what do you think you would need to find from the straight line in order to find out if it was normalto something?

for b) what is the usual procedure for finding a turning point of a curve?

 

[Architeuthis Dux]

Hello there! It seems like you are working on a calculus problem involving a straight line and a curve. To find the coordinates of point A, you can plug in the x-coordinate of A into the equation of the curve, y=4x^3+12x^2+9x-1, and solve for y. This will give you the coordinates of A as (x, y).

To find the turning points of the curve, you can take the derivative of the curve and set it equal to 0. This will give you the x-coordinates of the turning points. Then, you can plug these x-coordinates into the equation of the curve to find the corresponding y-coordinates.

To determine whether the turning points are maximum or minimum points, you can use the second derivative test. If the second derivative is positive, the point is a minimum point. If the second derivative is negative, the point is a maximum point.

Hope this helps! If you need further assistance, don't hesitate to ask. Good luck with your problem!