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Estimate $f(x)$ for $x=2,4,6,$ using the given values of $f^{\prime}(x)$ and the fact that $f(0)=50$.$$\begin{array}{l|r|r|r|r}\hline x & 0 & 2 & 4 & 6 \\\hline f^{\prime}(x) & 17 & 15 & 10 & 2 \\\hline\end{array}$$

$\begin{array}{|c|c|c|c|c|}\hline x & 0 & 2 & 4 & 6 \\\hline f^{\prime}(x) & 17 & 15 & 10 & 2 \\\hline f(x) & 50 & 84 & 114 & 134 \\\hline\end{array}$

Calculus 1 / AB

Chapter 6

Constructing Antiderivatives

Section 1

Antiderivatives Graphically and Numerically

Integration

Campbell University

Harvey Mudd College

University of Nottingham

Idaho State University

Lectures

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in this problem were given the derivative of a function. It's in disrepair years, and we're trying to estimate what the function value is at those values. So we have to It's your two or six and zero, the derivative 17 to its 15, but for 10 and six to And so now you want to try to estimate the function that each of these values So I told that zero starts at 50. But now we want to know what it is it too. And so the way we do that is we see that the derivative here is 17. So at X equals zero, the function in one stack was increased by about 17. But we go from zero the tube. So we go two steps, so we go 17 times to which 34. So the increase here will be 34. So 50 plus 34 is 84. Now we go from 2 to 4 and you see the slope here is 15. And so here we have to increase by 15. We have to do it twice because we go from 2 to 4223 So 84 plus 30 is going to be 114. And now finally we go through 46 with a slope of 10. So we dio 10 times, too. So 20 plus 1 14, there's 1 34.

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