derivative question.
(a) find an equation of the tangent line to the graph of y=g(x) at x=5 if g(5)=-3 and g'(5)=4
(b)if the tangent line to y=f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4)

Question

derivative question.
(a) find an equation of the tangent line to the graph of y=g(x) at x=5 if g(5)=-3 and g'(5)=4
(b)if the tangent line to y=f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4)

anonymous · Answer

y + 3 = 4 ( x -5)
=> y = 4x - 23

f ( 4) = 3
-> f'( 4) = 0
y - 2 = f'(4) x

rogue · Answer

Part A is correct.

f(x) includes the point (4,3), so f(4) = 3. f'(4) is the slope of the tangent, which is (3-2)/(4-0) = 1/4.

anonymous · Answer

I'm thinking of how to explain, but it's taking me forever, then I finally give it up!