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Math Help - Application of derivative

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    Application of derivative

    1. If , f(x)=4+3x-3x^2 find the equation of the line tangent to the curve f(x) at x=-5.
    The tangent line is y= ?

    2. A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 53 cm/sec. Find the rate at which the area within the circle is increasing after

    (A) 2 seconds Rate of increase = ?

    (B) 4 seconds Rate of increase = ?

    (C) 5 seconds Rate of increase = ?

    3. Let f(x)=-5x+7x^2. Then the expression f(x+h)-f(x)/h can be written in the form Ah+Bx+C, where A, B, and C are constants.

    I found that A= 7 B= 14 C= -5

    Use your answer from above to find the limit as h approaches 0 when f(x+h)-f(x)/h ??

    Finally, find each of the following: f '(1), f' (2), f ' (3)

    4. f(x)= sqrt(x+3)

    f'(1) ??
    f'(-2) ??
    f'(6) ??

    5. f(x)=1/x-1
    f ' (5) ??

    6. The slope of the tangent line to the curve y=3/x at the point (8,0.3750) is: ?
    The equation of this tangent line can be written in the form y=mx+b where m is: ?
    and where b is:?

    I just started calc this week so feel free to bash me for my stupidity..
    Last edited by Krizalid; January 29th 2009 at 04:26 PM.
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