Course:MATH102/Question Challenge/2010 December 02c

Question

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

(c) Let g(x) = 3ƒ(4x + 5). Given the information from previous parts of this question, there is one number b for which both g(b) and g'(b) can be found. What are b, g(b) and g'(b)?

Hints

This is one of hose rare math problems that includes irrelevant information (a "red herring"). The "both ... and" phrasing should help solvers recognize which pieces of given data are the most useful.

Solutions

Solution
We will assume that $4x+5=1$ $b=-1$ $g(b)=3f(1)=3(3)=9$ $g'(b)=3f'(4x+5)*4=12*f'(1)=12*(2)=24$ $b=-1$ $g(b)=9$ $g'(b)=24$