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2. Let k(x) be some function that is differentiable everywhere. We don't have a formula for k(x), but we do know the following values:
I k(0) = π/2
k'(0) = 1
k(1) = 2
k'(1) = -3
k(π/4) = -7
k'(π/4) = 5
k(T) = -√3/2
k'(T) = 4
Let F(x) = arctan(k(x)) and G(x) = k(arctan(x)). Using the values given above, find F'(1) and G'(1). Give exact answers, not approximations. Any angles are in radians, not degrees. Also note that you will use several of the given values of k(x), but not all of them.
2. Let k be some function that is differentiable everywhere. We don't have a formula for k, but we do know the following values:
I
k(0) = π/2
k'(0) = 1
k(1) = 2
k'(1) = -3
k(π/4) = -7
k'(π/4) = 5
k(T) = -√3/2
k'(T) = 4
Let F = arctan(x) and G = k(arctan(x)). Using the values given above, find F'(1) and G'(1). Give exact answers, not approximations. Any angles are in radians, not degrees. Also note that you will use several of the given values of k, but not all of them.