Calc

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Find h'(2), given that f(2)= -3, g(2)= 4, f'(2)= -2, and g'(2)= 7

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)

I have no idea how to plug these in. If someone could please show me how to go about one, I'm sure the rest would be nearly the same.

  • Calc -

    I'll do (c):
    h(x)=f(x)/g(x)

    use quotient rule in differentiation:
    d(u/v)=(v*du-udv)/v²

    so
    h'(2)=(g(x)*f'(x)-f(x)*g'(x))/g(x)²
    =(g(2)*f'(2)-f(2)*g'(2))/g(2)²
    =(4*(-2)-(-3)*7)/4²
    =13/16

    Check my work.

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