Let f (x) be a function which is continuous on [−7, 3] and differentiable on (−7, 3). Suppose that f ′(x) = 0 only when x = −3 and x = 1. Which of the following statements could be true about f (x)? (I) f (−3) is a local maximum and f (1) is a local minimum. (II) f (−3) is a local minimum and f (1) is a local maximum. (III) f (−3) and f (1) are both local maxima.
Let f (x) be a function which is continuous on [−7, 3] and differentiable on (−7, 3). Suppose that f ′(x) = 0 only when x = −3 and x = 1. Which of the following statements could be true about f (x)? (I) f (−3) is a local maximum and f (1) is a local minimum. (II) f (−3) is a local minimum and f (1) is a local maximum. (III) f (−3) and f (1) are both local maxima.
Let f (x) be a function which is continuous on [−7, 3] and differentiable on (−7, 3). Suppose that f ′(x) = 0 only when x = −3 and x = 1. Which of the following statements could be true about f (x)? (I) f (−3) is a local maximum and f (1) is a local minimum. (II) f (−3) is a local minimum and f (1) is a local maximum. (III) f (−3) and f (1) are both local maxima.
Let f (x) be a function which is continuous on [−7, 3] and differentiable on (−7, 3). Suppose that f′(x) = 0 only when x = −3 and x = 1. Which of the following statements could be true about f (x)?
(I) f (−3) is a local maximum and f (1) is a local minimum.
(II) f (−3) is a local minimum and f (1) is a local maximum.
(III) f (−3) and f (1) are both local maxima.
Please explain all steps
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 .
