Question

Let f (x) =x^(22/5) - 7cos(x) . Determine the largest for which is times continuously differentiable the 22/5 is a exponent.

Answer 1

The function f(x) = x^(22/5) - 7cos(x) is infinitely differentiable as both the power function x^(22/5) and the cosine function are differentiable for all x in their domains.

Step-by-step explanation:

The question asks to determine the largest number for which the function f(x) = x22/5 - 7cos(x) is continuously differentiable. The term x22/5 is a power function with a rational exponent, which is differentiable for all x in its domain. The cosine function, cos(x), is also known to be infinitely differentiable for all real numbers. Since the domain excludes division by zero or roots of negative numbers (which could occur for certain exponents), the function should be infinitely differentiable as both components are differentiable an infinite number of times.