Question

How many horizontal tangents may be drawn to each of the following cubic functions?
[Hint: You will need to differentiate and set the derivative equal to zero, then use the discriminant to find how many solutions this equation has.]
(a) y = x^3 + 5x^2 − 8x + 7

Answer 1

0= 3x^2 +10x -8

Answer 2

Continue for the answer.

Answer 3

so since your derivative is a quadratic, it will either have 0, 1, or 2 zeros

Answer 4

It will factor.

Answer 5

put dy/dx =0... find values of x.... then find double derivative nd put in value of x.. if dy/dx>0 or <0... then it represents a tangent

Answer 6

you can go ahead and solve, using the quadratic formula, or compute \(b^2-4ac\) which will tell you the number of zeros

Answer 7

oh... haha.. silly me... Thanks!!!

Answer 8

Had a mind blank :P

Answer 9

That's all right, it was a quick start.

Answer 10

Did you get the two points?

Answer 11

I got (2/3, 0) and (-4, 0)

Answer 12

yea, so it has 2 roots ^^

Answer 13

Yes

Answer 14

Thanks for your help

Answer 15

You're welcome, and as always good luck with your studies. You are making good progress.