The fum (4,4) 4 10 + 4 4 -2 2 4 6 8 12 to lamen...

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The fum (4,4) 4 10 + 4 4 -2 2 4 6 8 12 to lamen obiancoff SHT -4 (-4,-4) (8,-4) (12,-4) Graph of f 3. The figure above shows the graph of the piecewise-linear function f. For -4 x 12, the function g is defined by g(x) = f(t) dt. 2 (a) Does g have a relative minimum, a relative maximum, or neither at x = 10? Justify your answer. (b) Does the graph of g have a point of inflection at x = 4? Justify your answer. (c) Find the absolute minimum value and the absolute maximum value of g on the interval -4 x 12. Justify your answers. (d) For -4 x 12, find all intervals for which g(x) < 0. X f(x) f'(x) g(x) g'(x) 1 -6 3 2 8 2 2 -2 -3 0 3 8 7 6 2 6 4 5 3 -1 6. The functions f and g have continuous second derivatives. The table above gives values of the functions and their derivatives at selected values of x. (a) Let k(x) = f(g(x)). Write an equation for the line tangent to the graph of k at x = 3. (b) Let h(x): = g(x) f(x)* Find h'(1). (c) Evaluate f "(2x) dx. The fum (4,4) 4 10 + 4 4 -2 2 4 6 8 12 to lamen obiancoff SHT -4 (-4,-4) (8,-4) (12,-4) Graph of f 3. The figure above shows the graph of the piecewise-linear function f. For -4 x 12, the function g is defined by g(x) = f(t) dt. 2 (a) Does g have a relative minimum, a relative maximum, or neither at x = 10? Justify your answer. (b) Does the graph of g have a point of inflection at x = 4? Justify your answer. (c) Find the absolute minimum value and the absolute maximum value of g on the interval -4 x 12. Justify your answers. (d) For -4 x 12, find all intervals for which g(x) < 0. X f(x) f'(x) g(x) g'(x) 1 -6 3 2 8 2 2 -2 -3 0 3 8 7 6 2 6 4 5 3 -1 6. The functions f and g have continuous second derivatives. The table above gives values of the functions and their derivatives at selected values of x. (a) Let k(x) = f(g(x)). Write an equation for the line tangent to the graph of k at x = 3. (b) Let h(x): = g(x) f(x)* Find h'(1). (c) Evaluate f "(2x) dx.