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If a function f is differentiable at every point of its domain, what can be said about its continuity?
If a function f is differentiable at every point of its domain, what can be said about its continuity?
- It is continuous only at the midpoint of its domain.
- It is continuous only at the end points of its domain.
- It is not necessarily continuous at every point of its domain.
- It is continuous at every point of its domain. (correct)
What can be said about the product function f(x).g(x) if f(x) is differentiable at x = a and g(x) is not differentiable at x = a?
What can be said about the product function f(x).g(x) if f(x) is differentiable at x = a and g(x) is not differentiable at x = a?
- It can be differentiable at x = a. (correct)
- It is always differentiable at x = a.
- It is not defined at x = a.
- It is never differentiable at x = a.
If a function f(x) is differentiable at x = a, what can be said about its left-hand and right-hand derivatives at x = a?
If a function f(x) is differentiable at x = a, what can be said about its left-hand and right-hand derivatives at x = a?
- Both are equal and finite. (correct)
- One is equal and finite, the other is infinite.
- Both are unequal and infinite.
- Both are equal but infinite.
What is the condition for a function f(x) to be differentiable at a point P?
What is the condition for a function f(x) to be differentiable at a point P?
What is the right-hand derivative of f(x) at x = a, denoted by?
What is the right-hand derivative of f(x) at x = a, denoted by?
What is the set of points where the function f(x) = 1 - e^(-x) is differentiable?
What is the set of points where the function f(x) = 1 - e^(-x) is differentiable?
If f(x) and g(x) both are not differentiable at x = a, what can be said about the sum function f(x) + g(x)?
If f(x) and g(x) both are not differentiable at x = a, what can be said about the sum function f(x) + g(x)?
What is the condition for a function f(x) to be differentiable everywhere?
What is the condition for a function f(x) to be differentiable everywhere?
What is the left-hand derivative of f(x) at x = a, denoted by?
What is the left-hand derivative of f(x) at x = a, denoted by?
What can be said about the differentiability of the function f(x) = |x-1| at x = 1?
What can be said about the differentiability of the function f(x) = |x-1| at x = 1?
What is the condition for a function f(x) to be differentiable at a point a?
What is the condition for a function f(x) to be differentiable at a point a?
What can be said about the function f(x) if it is differentiable at every point in an open interval (a, b)?
What can be said about the function f(x) if it is differentiable at every point in an open interval (a, b)?
Which of the following functions is everywhere differentiable?
Which of the following functions is everywhere differentiable?
What is the relationship between the left-hand and right-hand derivatives of a function f(x) at a point a?
What is the relationship between the left-hand and right-hand derivatives of a function f(x) at a point a?
What is the geometric interpretation of the derivative of a function f(x) at a point a?
What is the geometric interpretation of the derivative of a function f(x) at a point a?
What can be said about the function f(x) = 1 + |x| at x = 0?
What can be said about the function f(x) = 1 + |x| at x = 0?
What is the derivative of the function f(x) = |x - 1| + |x - 3| at x = 2?
What is the derivative of the function f(x) = |x - 1| + |x - 3| at x = 2?
What can be said about the function f(x) = |x| at x = 0?
What can be said about the function f(x) = |x| at x = 0?
What is the condition for a function f(x) to be differentiable at a point a?
What is the condition for a function f(x) to be differentiable at a point a?
What can be said about the function f(x) = 1 - e^(-x) at x = 0?
What can be said about the function f(x) = 1 - e^(-x) at x = 0?
What can be said about the function f(x) = |x - 1| + |x + 1|?
What can be said about the function f(x) = |x - 1| + |x + 1|?
What can be said about the function f(x) = (x-1)|x-3|x+2|+cos(|x|) at x = 2?
What can be said about the function f(x) = (x-1)|x-3|x+2|+cos(|x|) at x = 2?
What is the derivative of f(x) = |x - 1| + |x + 1| at x = 2?
What is the derivative of f(x) = |x - 1| + |x + 1| at x = 2?
What is the value of f(0) for the function f(x) = xe^|x| if x ≠0 and f(x) = 0 if x = 0?
What is the value of f(0) for the function f(x) = xe^|x| if x ≠0 and f(x) = 0 if x = 0?
At what points is the function f(x) = |x - 1| + |x + 1| not differentiable?
At what points is the function f(x) = |x - 1| + |x + 1| not differentiable?
What can be said about the function f(x) = xe^|x| at x = 0?
What can be said about the function f(x) = xe^|x| at x = 0?
What can be said about the function f(x) = 2x - 1 at x = 0?
What can be said about the function f(x) = 2x - 1 at x = 0?
What is the limit of (f(x) - f(0))/h as h approaches 0 for the function f(x) = xe^|x| if x ≠0 and f(x) = 0 if x = 0?
What is the limit of (f(x) - f(0))/h as h approaches 0 for the function f(x) = xe^|x| if x ≠0 and f(x) = 0 if x = 0?
What is the left-hand derivative of f(x) = |x - 1| + |x + 1| at x = 1?
What is the left-hand derivative of f(x) = |x - 1| + |x + 1| at x = 1?
What can be said about the function f(x) = (x-1)|x-3|x+2|+cos(|x|) for x < 1 or x > 2?
What can be said about the function f(x) = (x-1)|x-3|x+2|+cos(|x|) for x < 1 or x > 2?
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