Fin fr an the eqvaTion of the line Tangm7 To The 3 Fnl tthe

& Fin/ f(r) an the eqvaTion of the line Tangm7 To The 3. Fnl tthe velative rare otf aT The Roond Three decsmal placts 4. Use the price-demand equation tofind E(p), the elasticity of demand. x = f(p) = 8,400-7p?

Solution

2) f(x) = x ( 4 - x)^3

f\'(x) = -4x^3 + 36x^2 - 96x + 64

f\" ( 2) = -4(2)^3 + 36(2)^2 - 96(2) + 64

= -16

now plugging this slope into point slope form

y - yo = m ( x - xo )

y - 0 = -16 ( x - 2)

y = -16x + 32

so, equation of line tangent to f(x) is y = -16x + 32