  # Consider the function q(x)=x11 −3x10 +2. Use the second derivative test to find the x-coordinates of all local maxima. If there are multiple values, give them separated by commas. If there are no local maxima, enter ∅.

Question

Consider the function q(x)=x11 −3x10 +2. Use the second derivative test to find the x-coordinates of all local maxima. If there are multiple values, give them separated by commas. If there are no local maxima, enter ∅.

check_circleExpert Solution
Step 1

To find the x-coordinates of all local maxima using the second derivative of the function.

Step 2

The given function is q(x) = x11–3x10+2.

Step 3

Second derivative test:

Let f be a real valued function defined and twice differentiable on an interval which contains a real number a as an interior point. Suppose that f′(a)=0, then:

(i) If f"(a)>0, then f has a local minimum at a.

(ii) If f"(a) <0, then f has a local maximum at a.

Use the above mentioned seco...

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