WitrynaIf f ( x) is differentiable then the derivatives from the left and right must be equal at x = 0. The derivative of x 1 + x at x = 0 is 1. The derivative of x 2 is 0 at x = 0. Thus f ( x) is not differentiable at x = 0. Share Cite Follow answered Oct 4, 2015 at 23:24 Rick 2,906 2 12 21 Add a comment You must log in to answer this question. Witryna13 maj 2016 · f ( n) ( x) = x then you have reached a dead end and this is indeed not differentiable further (because the derivative at x = 0 does not exist, although the function is continuous there). Any polynomial or simple exponent is infinitely differentiable (exponents cover sines and cosines as well)... UPDATE
real analysis - is the function $f$ differentiable at $(0,0 ...
Witryna12 kwi 2016 · Because f(x) = x is not differentiable at x = 0, then the derivative test does not apply there. Still it is pretty clear that if x ∈ ( − δ, δ) then f(0) ≤ f(x). Hence there is a local minimum at x = 0. There can even be a local minimum at x = x0 where the function is differentiable at x = x0 and f ′ (x0) ≠ 0. WitrynaLet f be a differentiable function \(x^2f(x)-x=4\int\limits_0^x tf(t)dt\) If f(1) = \(\frac{2}{3}\) then 18f (3) is. LIVE Course for free. ... Let f be a differentiable function defined on [0, π/2] such that f(x) > 0. asked Feb 10 in Mathematics by AnjaliJangir (56.4k points) jee main 2024 +1 vote. jdr office
real analysis - Proof: $f(x) = x $ is not differentiable at …
Witryna5 gru 2024 · Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Witryna8 lis 2016 · 1. To show that f is differentiable at ( 0, 0) you have to show that. f ( h) = f ( 0, 0) + ∇ f ( 0, 0) ⋅ h + o ( h ) for h ∈ R 2 in a neighbourhood of ( 0, 0) (here ⋅ denotes … WitrynaConsider the following statements.1. The function \\( f(x)= x \\) is not differentiable at \\( x=1 \\)2. The function \\( f(x)=e^{x} \\) is differentiable at \\( x... jdr joan of arc