generate a continuous and differentiable function f(x) with the below properties. f(x) is decreasing at x=−6 f(x) has a local minimum at x=−2 f(x) has a local maximum at x=2 Use calculus! Before specifying a function f(x), first determine requirements for its derivative f′(x). For example, one of the requirements is that f′(−2)=0 . If you want to find a function g(x) such that g(−9)=0 and g(8)=0, then you could try g(x)=(x+9)(x−8)
generate a continuous and differentiable function f(x) with the below properties. f(x) is decreasing at x=−6 f(x) has a local minimum at x=−2 f(x) has a local maximum at x=2 Use calculus! Before specifying a function f(x), first determine requirements for its derivative f′(x). For example, one of the requirements is that f′(−2)=0 . If you want to find a function g(x) such that g(−9)=0 and g(8)=0, then you could try g(x)=(x+9)(x−8)
generate a continuous and differentiable function f(x) with the below properties. f(x) is decreasing at x=−6 f(x) has a local minimum at x=−2 f(x) has a local maximum at x=2 Use calculus! Before specifying a function f(x), first determine requirements for its derivative f′(x). For example, one of the requirements is that f′(−2)=0 . If you want to find a function g(x) such that g(−9)=0 and g(8)=0, then you could try g(x)=(x+9)(x−8)
generate a continuous and differentiable function f(x) with the below properties.
f(x) is decreasing at x=−6
f(x) has a local minimum at x=−2
f(x) has a local maximum at x=2
Use calculus!
Before specifying a function f(x), first determine requirements for its derivative f′(x). For example, one of the requirements is that f′(−2)=0 .
If you want to find a function g(x) such that g(−9)=0 and g(8)=0, then you could try g(x)=(x+9)(x−8).
Please note that the bounds on the x-axis go from -6 to 6.
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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