# Thread: Horizontal tangents and Finding Derivative

1. ## Horizontal tangents and Finding Derivative

Find the horizontal tangents of the curve:
$y= x^4 - 7x^3 + 2x^2 + 15$

The lesson is about shortcut rules for derivatives.
Rules such as:
Power rule- $x^n = nx^(n-1)$
Power Rule of positive integer- same
Power Rule of negative integers- same
Product rule- derivative of (uv) = derivative of u + derivative of v
Constant function rule - derivative of any integer is 0
Quotient rule- don't know how to LaTex or describe. Don't need for this though.

I simplified the function to $x(4x^2 - 21x +4) = 0$ .
I know the goal of horizontal tangents is to get 0 = 0

There should be more, as that is the pattern of other problems.
Is there any way to figure it out algebraically? I'm very bad at trial and error. I found nothing else.

2. ## find the derivative - support graphically

Oops. Meant to make another thread. Oh well.

[tex](x^3 + x + 1)(x^4 + x^2 + 1)/MATH]

Using derivative shortcuts again.

Will paste them from other thread. ( see above)

3. Originally Posted by Truthbetold
Find the horizontal tangents of the curve:
$y= x^4 - 7x^3 + 2x^2 + 15$

The lesson is about shortcut rules for derivatives.
Rules such as:
Power rule- $x^n = nx^(n-1)$
Power Rule of positive integer- same
Power Rule of negative integers- same
Product rule- derivative of (uv) = derivative of u + derivative of v
Constant function rule - derivative of any integer is 0
Quotient rule- don't know how to LaTex or describe. Don't need for this though.

I simplified the function to $x(4x^2 - 21x +4) = 0$ .
I know the goal of horizontal tangents is to get 0 = 0

There should be more, as that is the pattern of other problems.
Is there any way to figure it out algebraically? I'm very bad at trial and error. I found nothing else.
yes, you got the right one.. the other two are just try to solve using quadratic equation.. Ü

4. Originally Posted by Truthbetold
Oops. Meant to make another thread. Oh well.
so, $D_x((x^3 + x + 1)(x^4 + x^2 + 1)) = (x^3 + x +1)D_x(x^4 + x^2 + 1) + D_x(x^3 + x + 1) (x^4 + x^2 + 1)$
$(x^3 + x +1)(4x^3 +2x) + (3x^2 +1)(x^4 + x^2 + 1)$