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- Compute f'(3) using the limit definition of derivative if f(x)=6x².Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and that f(2)= -2. Then f'(2) = ?19. Sketch a labeled graph of a function that fails to satisfy thehypothesis of the Extreme Value Theorem, and illustrateon your graph that the conclusion of the Extreme ValueTheorem does not necessarily hold
- But the Mean Value Theorem only applies if the function is continuous AND differentiable. Not differentiable at x=0 and x=2. So, I think it will work only in interval [2,4].If the function is defined y=2x when x<=3 and y=-x+9 when x>=3, is this function differentiable at x=3? Also, is this function continuous at x=3?as x -> infinity f(x) -> as x -> - infinity f(x) ->
- True or False The cube root function is odd and is decreasing on the interval (-∞,∞).draw the graph of a function f on [0, 4] with the given property. Jump discontinuity at x = 2 and does not satisfy the conclusion of the IVTSketch a graph of a function ƒ that is continuous on (- ∞, ∞) and has the following properties. ƒ'(x) > 0, ƒ"(x) > 0