# How do you use the second derivative test how do you find the local maxima and minima of #f(x) = 12 + 2x^2 - 4x^4#?

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To use the second derivative test to find the local maxima and minima of ( f(x) = 12 + 2x^2 - 4x^4 ):

- Find the first derivative of ( f(x) ) and set it equal to zero to find critical points.
- Find the second derivative of ( f(x) ).
- Evaluate the second derivative at each critical point.
- If the second derivative is positive at a critical point, the function has a local minimum at that point. If the second derivative is negative, the function has a local maximum at that point. If the second derivative is zero or undefined, the test is inconclusive.

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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.

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.

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.

- Consider the curve #y = (x^2- 2x+k)(x-6)^2 #, where #k# is a real constant. The curve has a maximum point at # x =3#. What is the value of #k#?
- What are the points of inflection, if any, of #f(x)= x^5 -2 x^3 - x^2-2 #?
- If #y = 3x^5 - 5x^3#, what are the points of inflection of the graph f (x)?
- What are the points of inflection of #f(x)=x^7/(4x-2) #?
- For what values of x is #f(x)=3x^3+2x^2-x+9# concave or convex?

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