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Math Help - Derivatives Help!

  1. #1
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    Derivatives Help!

    1)Find the slope of the tangent line to the graph at any point
    f(x)=sqrt (3-x)

    2) Find the slope of the tangetn line to the graph at given point and give an equation of the tangent line
    f(x)=3/2x at (1, 3/2)

    3)Let f(x)=x^2+6x
    a) Find the derivative f' of f
    b) Find the point on the graph of f where the tangent line to the curve is horizontal
    hint: find the value of x for which f'(x) =0

    I'm having problems with derivatives, can anyone teach me how to do these problems step by step! I appreciate it!
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by lemontea View Post
    1)Find the slope of the tangent line to the graph at any point
    f(x)=sqrt (3-x)

    2) Find the slope of the tangetn line to the graph at given point and give an equation of the tangent line
    f(x)=3/2x at (1, 3/2)

    3)Let f(x)=x^2+6x
    a) Find the derivative f' of f
    b) Find the point on the graph of f where the tangent line to the curve is horizontal
    hint: find the value of x for which f'(x) =0

    I'm having problems with derivatives, can anyone teach me how to do these problems step by step! I appreciate it!
    use the formula

    yf(x_0)=f'(x_0)(x-x_0)

    where f'(x)=\lim_{\Delta{x}\to{0}}\frac{f(x+\Delta{x})-f(x)}{\Delta{x}}

    or the derivative
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  3. #3
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    Quote Originally Posted by lemontea View Post
    1)Find the slope of the tangent line to the graph at any point
    f(x)=sqrt (3-x)

    2) Find the slope of the tangetn line to the graph at given point and give an equation of the tangent line
    f(x)=3/2x at (1, 3/2)

    3)Let f(x)=x^2+6x
    a) Find the derivative f' of f
    b) Find the point on the graph of f where the tangent line to the curve is horizontal
    hint: find the value of x for which f'(x) =0

    I'm having problems with derivatives, can anyone teach me how to do these problems step by step! I appreciate it!
    1) chain rule:
    sqrt (3-x) = (3-x)^(1/2)
    f'(x)=1/2*(3-x)^(-1/2)*(-1)=1/(2(3-x)^(1/2))

    2)is that a 3/(2x) or (3/2)x?

    3a)2x+6
    b)2x+6=0, x=-6/2=-3
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