For the function fx 3 e find f x Then find f 0 and f 1 Solut

For the function f(x) 3 e find f \"(x). Then find f \"0 and f \"(1)

Solution

f(x) = 3e^(-x^4) f\'(x) = 3e^(-x^4)(-x^4)\' [by chain rule] = 3e^(-x^4) (-4x^3) f\'\'(x) = 3(-4x^3) (e^(-x^4))\' + 3e^(-x^4) (-4x^3)\' [by product rule] = 3(-4x^3)e^(-x^4) (-4x^3) + 3e^(-x^4) (-12x^2) = 48x^6e^(-x^4) - 36x^2 e^(-x^4) f\'\'(0) = 0 - 0 =0 f\'\'(1) = 48e^(-1) - 36e^(-1) = 12e^-1 = 12/e