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Determine the values of a and b such that the following function is differentiable at 0. f ( x) = { a x 3 c o s ( 1 x) + b x + b, if x < 0 a + b x, if x ≥ 0 My solution For f to be
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A function is said to be differentiable if the derivative exists at each point in its domain. 👉 Learn how to determine the differentiability of a function.
e!You check if f is differentiable at the point x = 1. You begin with the left limit: lim x → 1 − f ′ ( x) = lim x → 1 − 2 x = 2 ⋅ 1 = 2 Next, the right limit: lim x → 1 + f ′ ( x) = lim x → 1 + − 2 = − 2 Because
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