# How do you find the slope of the secant lines of #f(x) = 7x^2# at #(4, f(4))# and #(4+h, f(4+h))#?

The slope is

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To find the slope of the secant line between two points on the function ( f(x) = 7x^2 ) at ( (4, f(4)) ) and ( (4+h, f(4+h)) ), you use the formula for slope:

[ \text{Slope} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} ]

where ( (x_1, f(x_1)) ) and ( (x_2, f(x_2)) ) are the coordinates of the two points.

For the given function ( f(x) = 7x^2 ), ( f(4) ) is ( 7 \times 4^2 ), and ( f(4+h) ) is ( 7 \times (4+h)^2 ).

So, the slope of the secant line is:

[ \text{Slope} = \frac{7 \times (4+h)^2 - 7 \times 4^2}{4+h - 4} ]

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