d f/dx=2x+6
f(x)=x^2+6x + k
3=6^2+6*6+k
k= -72+3=-69
f(5)=5^2+6*5-69
f(5)=25+30-69= ... you do it.
Given that the graph of f(x) passes through the point (6,3) and that the slope of its tangent line at (x,f(x)) is 2x+6, what is f(5)?
2 answers
f'(x)=2x+6
Integrate to get the graph's function:
f(x)=x^2+6x+c
where c is the constant of integration.
Sub in the pt (6,3) to solve for c and hence have a fully-defined function for the graph.
Finally, sub x=5 into the function to find f(5).
Integrate to get the graph's function:
f(x)=x^2+6x+c
where c is the constant of integration.
Sub in the pt (6,3) to solve for c and hence have a fully-defined function for the graph.
Finally, sub x=5 into the function to find f(5).