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Mean Value theorem is applicable to the and continuous in open interval (a, b) b) Functions continuous in closed interval only and having same value at point ‘a’ and ‘b’ c) Functions continuous in closed interval and differentiable in open interval (a, b) d) Functions differentiable in open interval (a, b) only and having same value at point ‘a’ and ‘b’
Rolle’s theorem is applicable to the and continuous in open interval (a, b) only and having same value at point ‘a’ and ‘b’ b) Functions continuous in closed interval only and having same value at point ‘a’ and ‘b’ c) Functions continuous in closed interval and differentiable in open interval (a, b) only and having same value at point ‘a’ and ‘b’ d) Monotonically Increasing funtions
Given the following statements about a function f : R → R , select the right option:
P: If f(x) is continuous at x = x0, then it is differential at x = x0.
Q: If f(x) is continuous at x = x0, then it may not be differentiable at x = x0.
R: If f(x) is differentiable at x = x0, then it is also continuous at x = x0.
Find the value of c(a point where slope of a atangent to curve is zero) if f(x) = Sin(x) is continuous over interval and differentiable over interval (0, π) and c ∈(0,π)
Find the value of c if f(x) = x(x-3)e3x, is continuous over interval and differentiable over interval (0, 3) and c ∈(0,3)
Find the value of c if f(x) = sin3(x)cos(x), is continuous over interval and differentiable over interval (0, π⁄2) and c ∈(0, π⁄2)
Find the value of ‘a’ if f(x) = ax2+32x+4 is continuous over and differentiable over (-4, 0) and satisfy the Rolle’s theorem. Hence find the point in interval (-2,0) at which its slope of a tangent is zero
A differentiable activation function makes the function computed by a neural network differentiable and the back propagation algorithm is applicable to it.
Consider the following statements: 1. The function f(x) = | x | is not differentiable at x = 1 2. The function f(x) = ex is differentiable at x = 0. Which of the above statements is/are correct?
Find point c between where, the slope of tangent to the function f(x) = x2+3x+2 at point c is equals to the slope of a line joining point (-1,f(-1)) and (6,f(6)). (Providing given function is continuous and differentiable in given interval).