Question

Find the area of the triangle formed by the x-axis and the lines tangent and normal to the curve
f(x)=7x-3x^2 at the point (2,2)

Answer 1

slope of tangent = f'(x) = 7 - 6x = 7 -12 = -5 at (2,2)
slope of the normal = 1/5
equation of tangent is y - 2 =-5(x-2)
and of normal is y - 2 = 1/5(x-2)
intercept on x-axis of tangent is 2.4
intercept on x-axis of normal is 5
so the length of base of the triangle is 5-2.4 = 2.6

area of triangle = 1.3 * 2 = 2.6

Answer 2

Thanks Jimmyrep! just saw this now. will go through it to make certain I understand.