Let fbe a function which is continuous on the interval [0,5], twice differentiable on (0,5), and...

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Let fbe a function which is continuous on the interval [0,5], twice differentiable on (0,5), and has f"(x) <0 for all xe(0,5). Which of the following are (i) always true, or (ii) never true, or (iii) sometimes true? Justify your answers. (a) For some 0 <c <5, f'(c)= ). (b) fhas an inflection point somewhere in (0,5). (c) fachieves its maximum at x=5. (d) f achieves its minimum at x=5. Let fbe a function which is continuous on the interval [0,5], twice differentiable on (0,5), and has f"(x) <0 for all xe(0,5). Which of the following are (i) always true, or (ii) never true, or (iii) sometimes true? Justify your answers. (a) For some 0 <c <5, f'(c)= ). (b) fhas an inflection point somewhere in (0,5). (c) fachieves its maximum at x=5. (d) f achieves its minimum at x=5.