Homework Soursesuppose that f23 g24 f22 and g27 find the h2 a hx5fx4gx b hx
suppose that f(2)=-3, g(2)=4, f\'(2)=-2 and g\'(2)=7. find the h\'(2).
a) h(x)=5f(x)-4g(x)
b) h(x)=f(x)g(x)
c) h(x)=f(x)/g(x)
d) h(x)=g(x)/1+f(x)
a) h(x)=5f(x)-4g(x)
b) h(x)=f(x)g(x)
c) h(x)=f(x)/g(x)
d) h(x)=g(x)/1+f(x)
Solution
a) h\'(2) = 5f\'(2) - 4g\'(2) = 5*(-2) - 4*7 = -38
b) h\'(2) = f\'(2)g(2) + f(2)g\'(2) = -2*4 - 3*7 = -29
c) h\'(2) = (f\'(2)g(2) - f(2)g\'(2))/g(2)^2 = (-8+21)/16 = 13/16
d) h\'(2) = ((1+f(2))g\'(2) - f\'(2)g(2))/(1+f(2))^2 = (-2*7+2*4)/(-2)^2 = -6/4 = -3/2
