math

The gradient of the tangent to the curve y= ax^3 + bx at the point ( 1, 1) is -5. Calculate the values of a and b

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  1. We need to find a and b, so we will look for two equations.

    The first one is simply the point (1,1), which tells us that 1=y(1), or
    1=a(1^3)+b(1)=a+b, or
    a+b=1............(1)

    The second one is the fact that the gradient (dy/dx) at (1,1)=-5.
    Since dy/dx = 3ax²+b, we have
    -5 = 3a(1^2)+b = 3a+b
    or
    3a+b = -5...........(2)

    Solve for a and b given the system of equations:
    a+b=1............(1)
    3a+b = -5...........(2)

    You can solve by elimination.

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  2. a=-3 ,b=4

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