Home > Calculus > Analyzing Concavity of a Function

How do you determine whether the function #y=x^2 # is concave up or concave down and its intervals?

Answer 1

#y=x^2# is concave up with an interval of #(-oo,+oo)#

A polynomial function is concave up (opens upward) if the coefficient of #x^2# is greater than #0#. If the coefficient of #x^2#is greater than #0# then #yrarr+oo# as #xrarr+-oo#

Conversely if the coefficient of #x^2# is less than #0# the parabola opens downward.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Elijah Abram

To determine whether the function ( y = x^2 ) is concave up or concave down, you can examine its second derivative.

Find the second derivative of the function ( y = x^2 ) with respect to ( x ).

[ \frac{{d^2y}}{{dx^2}} = 2 ]

Since the second derivative is a constant (in this case, 2), you can conclude that the function ( y = x^2 ) is concave up everywhere.

Therefore, the function ( y = x^2 ) is concave up for all real numbers ( x ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.