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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

Solution Preview

Using the slope Predictor formula {f(x+h) - f(x)} / h , we get
the slope m of the tangent as
And as you have calculated right, the value of the function at x=3 is f(3)=96.

Let the equation to ...

Solution Summary

The equation of a tangent to a curve is found using the slope-predictor formula. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.