Determine whether the statement is true or false. If it is false, explain why or

Question

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If a function is differentiable at a point, then it is continuous at that point. True. False. f(x) = |x - 2| is differentiable, but not continuous at x = 2. False. f(x) = 1/x is differentiable, but not continuous at x = 1. False. F(x) = x^2 is differentiable, but not continuous at x = 0. Find the slope of the tangent line to the graph of the function at the given point. g(x) = 11 - x^2; (1, 10)

Explanation / Answer

1.) True, as it is required for the function to be continous when it is differentiable.

2.)

g(x)=11-x^2

g'(x)=-2x

g'(1)=-2

Hence, the slope of the tangent at point (1,10) is -2.

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