Chapter 5.2, Problem 30E

determine a function by being given the function’s first derivative and an initial condition for the function. Discuss how you would determine an original function if you were given the second derivative of the function as well initial conditions on the first derivative and original function.

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Derivative. Please explain.

Graph of f" +x 8. The graph of f", the second derivative of the function f, is shown above. Which of the following could be the graph of f?

(1 point) Use the given graph of the function f to find the following values for f1. 1.(-4) = 2. f'(-3) = 3. f (0) = 4. (2) = 5. f '(4) =

Let f (t) = sin t. Use the results of Section 3.2 to find the exact values for the derivative of f at the given numbers. You can use 2**.5 for V2 and 3**.5 for v3. f r(즐)-

Each graph below represents a function f(r). On the same axes, sketch the graph of the derivative f'(r). If you are writing on your own paper, clearly draw f ( 2 ) and the coordinate axes, then draw and label f'(x). फ -5 -5 0 M -5 10

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Use definition to compute the derivative of f(x)=V3x+1. You may not use any calculus formulas.