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) attains a local maximum 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 case, f(a) attains a local maximum value f(x) at x=a .
