Thread: Differentiation.. the values of x for which dy/dx > 0

Given that , the values of x for which

This is what I'm thinking.

First differentiate. Then put the sign then 0. You will get

Is this right?

Originally Posted by jgv115

Given that , the values of x for which

This is what I'm thinking.

First differentiate. Then put the sign then 0. You will get

Is this right?

Yes,
from there you find the range of x for which

In the case of quadratics, you can alternatively find the axis of symmetry.
The co-efficient of is positive, so the graph is U-shaped.
Hence the slope of the tangent is at or after the minimum,
which occurs halfway between the roots or at the roots in the case of a double root.



Double root at x=3, so the tangent has a positive slope after x=3.