Course:MATH102/Question Challenge/2010 December 02a

Question

Suppose the tangent line to the graph of y = ƒ(x) at x = 1 is y = 2x + 1, and ƒ(3) = 2.

(a) What are the values of ƒ(1) and ƒ'(1)?

Solutions

[show]Solution
$f'(1)$ is given by the slope of the tangent line</math> therefore: $f'(1)=2$ We can solve for $f(1)$ with algebra</math> $y=2(1)+1$ $y=f(1)=3$ $f(1)=3$ and $f'(1)=2$