Determine whether following function is differentiable at the given point.f(x) = cos(x)x2 + 1, x = 0
Question
Determine whether following function is differentiable at the given point.
The function is given as:
Evaluate at the point:
Solution
To determine if the function is differentiable at the given point, we need to find the derivative of the function and then evaluate it at the given point.
Step 1: Find the derivative of the function The function is a product of two functions, cos(x) and x^2 + 1. So, we will use the product rule to find the derivative. The product rule states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function.
The derivative of cos(x) is -sin(x) and the derivative of x^2 + 1 is 2x.
So, the derivative of the function is:
f'(x) = cos(x
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