Relative Max ( 2nd derivative test)
f'(x)=0f(x) < 0Backwards
The second derivative test is a method used to find relative maximum points when you have a function that is twice differentiable. This test uses the second derivative of the function to determine the behavior of the graph of the function near a point.
Here are the steps to find relative max using 2nd derivative test:
Step 1: Find the first derivative of the given function.
Step 2: Find the second derivative of the given function.
Step 3: Find the critical points of the given function by solving f ‘(x) = 0.
Step 4: Test the sign of the second derivative of the function at each critical point. If the second derivative is positive, then we have a relative minimum point, and if it is negative, then we have a relative maximum point. If the second derivative is zero, then the test fails.
Step 5: Interpret the results. If the second derivative is negative at a critical point, then we have a relative maximum at that point. If the second derivative is positive at a critical point, then we have a relative minimum at that point.
Thus, using the second derivative test, we can determine whether a critical point is a relative maximum or a relative minimum.
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