Question

does this function x^3-x^2+4x-3 has a local maximum and a local minimum?

Answer 1

no its derivative is never equal to 0

Answer 2

Nearly, the derivative is only equal to 0 for complex values.

Curve is monotonic increasing with a point of inflection.

Answer 3

but it does has concavity and point of inflection right?

Answer 4

all cubic functions have an inflection point

Answer 5

so scond derivative would be 6x-2 and the inflection point 1/3

Answer 6

Yes, convex and concave for which you can test with the second derivative.

Answer 7

Just test either side of the point of inflection.

Answer 8

'the inflection point 1/3'

1/3 is not a point

Answer 9

so 0.33?

Answer 10

this is a function in R^2

a point is an ordered pair (a,b)

Answer 11

oh ok so you mean (1/3,f(1/3))

Answer 12

yes