# Slope Predictor Formula : Finding a Tangent Line to a Curve

1. Apply the slope-predictor formula to find the slope of the line tangent to

y = f(x) = (2x+4)2 - (2x-4)2. Then write the equation of the line tangent to the graph of f at the point (3, f(3)).

My attempt...

I found y first by:

f(x) = (2x+4)2 - (2x-4)2

f(x) = (4x2+16x+16) - (4x2-16x+16)

f(x) = (4x2+16x+16) + (-4x2+16x-16) = 32x

f(x) = 32x

y = f(3) = 32(3) = 96

x=3 is given and the equation of the line with slope m is given as:

y = mx + c

so, 96 = m3 + c

I'm stuck trying to find m. I need to use the slope predictor formula f(x+h) - f(x) / h

I'm not sure if this is the right way. Can someone show me how to calculate m using the slope predictor formula?

m(x) = (2x+4)2 - (2x-4)2

m(x) = ((2(x+h) + 4) 2 - (2(x+h) - 4) 2) - ((2x+4)2 - (2x-4)2) / h

m(x) = ((2x+2h+4) 2 - (2x+2h-4) 2 ) - ((2x+4)2 - (2x-4)2) / h