Question

Let f be a differentiable function such that f(3) = 2 and f'(3) = 5. If the tangent line to the graph of f at x = 3 is used to find an approximation to a zero of f, that approximation is?

So confused

Answer 1

y=mx+b f'(3)=5 means m=5
y=5x+b but f(3)=2 means
2=5*3+b, or b= -13

tangent line y= 5x-13
so the zero is 0=5x-13 x=13/5

Answer 2

That approximation is the intersection of
the tangent and X-axis.
The equation of the tangent:
y-2=5(x-3)
If y=0 then x=13/5

Answer 3

nice work, Mgraph.