function f(x) has the following properties: 1) f(x) as critical points at x=4 and x=7, 2) f'(x)is negative to the left of 4 and negative to the right of 7 3)f′(x) is positive between 4 and 7, then which of the following is true? f(x) attains a minimum at x=7 but f(x) has neither a maximum nor a minimum at x=4. f(x) attains a local maximum at x=4 and a local minimum at x=7. f(x) attains a local minimum at x=4 and a local maximum at x=7. None of the given statements about maxima and minima about f(x) are correct.
function f(x) has the following properties: 1) f(x) as critical points at x=4 and x=7, 2) f'(x)is negative to the left of 4 and negative to the right of 7 3)f′(x) is positive between 4 and 7, then which of the following is true? f(x) attains a minimum at x=7 but f(x) has neither a maximum nor a minimum at x=4. f(x) attains a local maximum at x=4 and a local minimum at x=7. f(x) attains a local minimum at x=4 and a local maximum at x=7. None of the given statements about maxima and minima about f(x) are correct.
function f(x) has the following properties: 1) f(x) as critical points at x=4 and x=7, 2) f'(x)is negative to the left of 4 and negative to the right of 7 3)f′(x) is positive between 4 and 7, then which of the following is true? f(x) attains a minimum at x=7 but f(x) has neither a maximum nor a minimum at x=4. f(x) attains a local maximum at x=4 and a local minimum at x=7. f(x) attains a local minimum at x=4 and a local maximum at x=7. None of the given statements about maxima and minima about f(x) are correct.
If a function f(x) has the following properties: 1) f(x) as critical points at x=4 and x=7, 2) f'(x)is negative to the left of 4 and negative to the right of 7 3)f′(x) is positive between 4 and 7, then which of the following is true?
f(x) attains a minimum at x=7 but f(x) has neither a maximum nor a minimum at x=4.
f(x) attains a local maximum at x=4 and a local minimum at x=7.
f(x) attains a local minimum at x=4 and a local maximum at x=7.
None of the given statements about maxima and minima about f(x) are correct.
f(x) attains a minimum at x=4, but f(x) has neither a maximum nor a minimum at x=7.
Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .
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