WebThe general fact is: Theorem 2.1: A differentiable function is continuous: If f(x)isdifferentiableatx = a,thenf(x)isalsocontinuousatx = a. Proof: Since f is differentiable … WebShow that the following function f(x) is differentiable at x=0 : f(x)={x2sin(x1)0:x=0: ... 3. Show that the following function f ( x ) is differentiable at x = 0 : f ( x ) = { x 2 sin ( x 1 ?

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WebLet f (x) = x2 if x ≥ 0 and f (x) = 0 if x < 0. (a) Show that f is differentiable at x = 0. (b) Find f′ (x) for all x ∈ R and sketch the graph of f. (c) Is f′continuous on R? Is f′ differentiable on R. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer WebShow that the function f(x)=∣x∣ is not differentiable at the point x=0 Easy Solution Verified by Toppr f(x)=∣x∣ ={+x,−x,x≥0x<0 f(x)={+1,−1.x≥0x<0 At x=0 Left hand derivative =−1 Right hand derivative =+1 ∴ L.H.D = R.H.D So, f(x)=∣x∣ is not differentiable at x=0. Video Explanation Was this answer helpful? 0 0 Similar questions the man of twist and turns

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WebA function f (x) is differentiable at the point x = a if the following limit exists: lim h→0 f (c+h)−f (c) h lim h → 0 f ( c + h) − f ( c) h Example: Consider the absolute value function given by f (x) = x We will determine if this function is differentiable at c = 0 or not. Webx^2 is a parabola centered at the origin....If you take its derivative you get 2x, therefore the derivative of f(x) at 0 would be equal to 0... or you can write as f'(0) = 0....It is a parabola … WebThe Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f' (c) is equal to the function's average rate of change over [a,b]. the man of twists and turns