+128474 y(x) = x(x + 3) = x^2 + 3x
(a) We have this difference quotient
[ (x + h)^2 + 3(x +h) - ( x^2 + 3x) ]
_________________________ simplify
h
[ (x^2 + 2xh + h^2 + 3x + 3h) - (x^2 + 3x) ]
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h
[ 2xh + h^2 + 3h - ]
________________
h
h [ 2x + h + 3 ]
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h
2x + h + 3 and when h → 0, we have
2x + 3 ...... this is the gradient at any x value on the curve
(b) The gradient of the curve at (-5, 10) is
2(-5) + 3 = -7
