Suppose that f(-1) = 3 and that f\'(x) = 3 for all x. Must f(x) = 3 for all x? G

Question

Suppose that f(-1) = 3 and that f'(x) = 3 for all x. Must f(x) = 3 for all x? Give reasons for your answer. A. No. Since f'(x) = 3 for all x, f is a linear function with slope 3. The value of f is different for all values of x. B. Yes. Since f(-1) = 3, f is a constant function with slope 3. The value of f is the same for all values of x. C. Yes. Since f'(x) = 3 for all x, and 3 is a constant, the value of f equals f(-1) for all values of x. D. No. Since f(-1) = 3 is greater than -1, f(x) is greater than x for all values of x.

Explanation / Answer

A,

No,

f'(x) = 3, means f is a linear function with a slope of 3

value of f is different for all values of x,

Assume f(x) = ax + b

f'(x) = a, so a = 3,

f(x) = 3x + b

f(-1) = 3 = 3*(-1) + b

b = 6

f(x) = 3x + 6

Correct option is A.

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