A diagram shows the graph of y=4+4x-x^2. The tangent to the curve at the point (3,7) cuts the axes at A and B. work out the area of triangle OAB answer

Question

A diagram shows the graph of y=4+4x-x^2. The tangent to the curve at the point (3,7) cuts the axes at A and B. work out the area of triangle OAB answer

Answer 1

y'(3) = -2 = slope of the tangent at (3,7)

y'(x) = -2x + 4

y'(3) = -2(3)+ 4 = -6+4 = -2

the equation of the tangent line through that point is

y=-2x+b, plug in the point to get b

7=-2(3) + b

b = 13

the triangle is 13 by 13/2

area is 13(13/2)/2 = 169/4 = 42.25