Question

Find the inflection points and local extrema of f(x)=8sinx−42–√x with domain −π/2≤x≤2π . then find the intervals on which f(x) is concave up and concave down.

Answer 1

The answer to finding inflection points and local extrema involves using first and second derivatives of the function, then applying derivative tests to determine their nature and intervals of concavity.

Step-by-step explanation:

The answer to finding the inflection points and local extrema of a given function involves calculating its first and second derivatives, and then analyzing the sign changes in these derivatives.

To find the local extrema, we need to set the first derivative equal to zero and solve for the critical points, followed by using the first derivative test or the second derivative test to determine if these points are maxima or minima.

For finding inflection points, we set the second derivative equal to zero to find potential inflection points, and check for a sign change in the second derivative to confirm.

We identify intervals on which the function is concave up by finding where the second derivative is positive, and concave down when the second derivative is negative.