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?

Using the slope Predictor formula {f(x+h) - f(x)} / h , we get
the slope m of the tangent as
m={32(x+h)-32x}/h=32.
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.

Given f(x) = 2/(x-1) use the four step process to find a slope-predictor function m (x). Then write an equation for the linetangent to the curve at the point x = 0.

Find the point on the graph of the given function at which the slope of the tangentline is the given slope.
f(x)= (x^3) + (9x^2) + 36x +10
slope of the tangentline = 9
What is the ordered pair?

The curve C has equation: y = x^3 - 2x^2 - x + 9, x>0
The point P has coordinates (2,7).
(a) Show that P lies on C.
(b) Find the equation of the tangent to C at P, giving your answer in the form of y = mx+c, where m and c are constants.
The point Q also lies on C.
Given that the tangent to C at Q is perpendicular to

Find the slope and the equation of the tangentline to the graph of the function at the given value of x.
f(x) = x^4 - 5x^2 + 4
x = -2
The slope of the tangentline = ?
The equation of the tangentline is y= ?

Find the curve that passes through the points (3, 2) and has the property that if the tangentline is drawn at any point P on the curve, then the part of the tangentline that lies in the first quadrant is bisected at P.

See attached file for full problem description.
1. Apply the slopepredictorformula to find the slope of the linetangent to y = f(x) = (2x + 4)^2 - (2x -4)^2. Then write the equation of the linetangent to the graph of f at the point (3, f(3)).
2. Find all points on the curve y = (x+4)(x-5) at which the tangentline is horiz