<p>Hey ppl. I have a problem for you to solve. Given f(12)=200 and f'(12)=-6. use these givens to estimate f(14)? Is it 188? Thanks a lot.</p>
<p>is that all there is to the problem? no graph? in this case, you can't really tell for sure since you don't know if the derivative is constant. it could be a large number of things, so technically any number is correct.</p>
<p>Use the tangent line of f at (12,f(12)) to approximate f(14).</p>
<p>y=mx+b
200=-6<em>12+b
b=272
f(14)=-6</em>14+272=188</p>
<p>use slope formula for this
so
(200-x)/(12-14)=-6 x=188
this only gives enough information to approximate by using the derivative, and as the number exceeds twelve, then the error increases.</p>
<p><em>slaps myself</em> APPROXIMATE. see? that's why i got a 780 in math, i just don't read. if it is appromixation, yes it would be 188.</p>
<p>yup tongo and mathgeeks methods are both right.</p>