If f(1)=13 and f'(x)<=7 for 1<=x<=4, what is the largest possible value of f(4)?
This question is a bonus on an assignment for me. We haven't covered how to do this. I don't really need the answer to the question, just the method by which to get an answer to questions like these. Thanks in advance.
This question is a bonus on an assignment for me. We haven't covered how to do this. I don't really need the answer to the question, just the method by which to get an answer to questions like these. Thanks in advance.
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If f'(x) is less than or equal to seven on the interval [1, 4], then the maximum value for
f(4) can be found by drawing a straight line with a slope of 7 from f(1). Because the slope of a tangent to the curve is always less than or equal to 7, this line marks the max value of the function on the interval. You can find the equation of a line with slope 7 through (1, 13), then find that equation to find the max value of f(4).
f(4) can be found by drawing a straight line with a slope of 7 from f(1). Because the slope of a tangent to the curve is always less than or equal to 7, this line marks the max value of the function on the interval. You can find the equation of a line with slope 7 through (1, 13), then find that equation to find the max value of f(4).
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f(4)-f(1) <= f'(x)*3
so f(4) <= 13 + 21 = 34
so f(4) <= 13 + 21 = 34