Find which value of x horizontal Tangent Line

Find which value of x....horizontal Tangent Line

Homework Statement

What is given is F(x)= -4/(x-3)(x+4) and the problem asks for to find the value of x where f(x) has a horizontal tangent line.

Homework Equations

I read somewhere else on these forms that using the quotient rule is the key, and that you make F'(x) to be equal to 0. If this is correct, I need some clarification on how it'd be put into the formula.

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rock.freak667
Homework Helper

Well yes a horizontal tangent line, means that the gradient of the tangent at that point is zero, so F'(x)=0.

But you don't necessarily need to use the quotient rule, the chain rule would suffice as well.

So first find, F'(x)

Well yes a horizontal tangent line, means that the gradient of the tangent at that point is zero, so F'(x)=0.

But you don't necessarily need to use the quotient rule, the chain rule would suffice as well.

So first find, F'(x)
So, that means the left side is euqal to zero, or is every where (including left side) that is f '(x) is equal to zero. Or, am I looking for the derivative, but anywhere in the formula I see that has f ' (x) is simply zero. Thanks in advance.

rock.freak667
Homework Helper

Just find the expression for F'(x) and just equate that expression to zero and solve for x.