Home › AP EAMCET › Mathematics › Differentiation Rules › Which statement about continuity and differentia…
Which statement about continuity and differentiability is correct?
AA jump function can be differentiable
BDifferentiable functions are continuous
CEvery function is differentiable
DEvery continuous function is differentiable
Answer & Solution
Correct answer: B. Differentiable functions are continuous
Differentiability at a point forces continuity there, but a corner like |x| is continuous without being differentiable.
Related questions
Near a point, the derivative supplies which kind of approximation of the function?For f(x) = 2x^3 - 5x + 1, the slope at x = 1 isRewriting 1/x^2 as x^(-2), its derivative becomesFor positive x, the product x^3 ln x has slope functionThe curve y = x e^x has slope at the origin equal toSquaring the sine, y = sin^2 x, gives a slope function equal toThe common logarithm y = log10 x, for x > 0, has slope functionA bell-type curve y = e^(x^2) changes with x at the rate