Suppose the line tangent to the graph of f at x=3 is y=2x+1and suppose y=3x-3 is the line tangent to the graph of g at x=3. Find an equation of the tangent line to the following curves at x=3.
a. f(x) + g(x)
b. f(x) - 3g(x)
c. 4f(x)

Question

Suppose the line tangent to the graph of f at x=3 is y=2x+1and suppose y=3x-3 is the line tangent to the graph of g at x=3. Find an equation of the tangent line to the following curves at x=3. 
a. f(x) + g(x)
b. f(x) - 3g(x)
c. 4f(x)

anonymous · Answer

NEED HELP!

anonymous · Answer

ok you know that 
$$f(3)=7,g(3)=6,  f(3)+g(3)=13$$and you know that the slope will be 2 + 3 = 5 so you can use the point- slope formula to find the equation

anonymous · Answer

its it clear how you know these things?

anonymous · Answer

yess

anonymous · Answer

ok then are you good from there?  because the others work the same way.  you know 
$$(f+g)'=f'+g'$$
$$(f+g)'(3)=f'(3)+g'(3)=3+2=5$$ and 
$$(f+g)(3)=6+7=13$$ so use 
$$y-13=5(x-3)$$ for your first answer

anonymous · Answer

i think i might be good for the rest, thank you

anonymous · Answer

i got 5x+3 for b but thats not right. could you show me the steps and the answesr cause im not sure what i did wrong