# Use the second derivative test to find the x-coordinates of all local minima given the following function.p(x)=x3 +5x2 +10If there are multiple values, give them separated by commas. If there are no local minima, enter ∅.

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Use the second derivative test to find the x-coordinates of all local minima given the following function.

p(x)=x3 +5x2 +10

If there are multiple values, give them separated by commas. If there are no local minima, enter ∅.

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Step 1

We have to find local minimum of p(x).

P(x) is given as:

Step 2

We will use following rules of derivative to find p'(x) and p''(x).

Rules are given below:

Step 3

Second derivative test :

If we have critical point let's say x=a and second derivative at x=a gives positive value it means p(x) has minimum at x=a.

Critical points are those point where first derivative equals to zero  or undefined in given d...

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### Calculus 