Verify the Rolle’* Theorem for functions on the indicated intervals: f(x) = e^x cos x on [-π/2, π/2]

Question 1

Verify the Rolle’* Theorem for functions on the indicated intervals: f(x) = ex cos x on [-π/2, π/2]

Question 2

As we know that exponential and cosine functions are continuous and differentiable on R.

Let us find the values of the function at an extreme

Here, f'(-π/2) = f(π/2), therefore there exist a c ∈ (-π/2,π/2) such that f'(c) = 0.

Let us find the derivative of f(x)

Here, f'(c) = 0,

Thus, Rolle'* theorem is verified.

kratos · Answer 1 · 2020-07-16T03:37:55+0000

As we know that exponential and cosine functions are continuous and differentiable on R.

Let us find the values of the function at an extreme

Here, f'(-π/2) = f(π/2), therefore there exist a c ∈ (-π/2,π/2) such that f'(c) = 0.

Let us find the derivative of f(x)

Here, f'(c) = 0,

Thus, Rolle'* theorem is verified.

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