For the function f(x) = 4+ 12x²-x³, find the local extrema. Then, classify the local extrema using the second derivative test. Be sure to state the second derivative values at the extrema. Hint: extrema is a point on a graph. A/

Determine the relative extrema using the Second derivative test. Find the point of inflection y = x(x² - 5)²

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Draw a graph to match the description. Answers will vary. F(x) has a positive derivative over (-, -5) and (-5, 4) and a negative derivative over (4, o), and a derivative equal to 0 at x = -5.

Cacaulte the derivative

Find equations of the tangent line and the normal line to the graph of the function f(x) = 5x² + 8 at the point (-3,53). %3D (Express numbers in exact form. Use symbolic notation and fractions where needed. Let y = f(x) and give the equations in %3D terms of y and x.) tangent line equation: normal line equation: Select the image containing the graph of the function, the tangent line, and the normal line at the indicated point on the same set of coordinate axes.

Differentiate. f (t) = 2/t - 3t3