Slope Formulas

For polynomial functions f(x)=a+bx+cx²+dx³ of degree 3 or less, the formula for the slope of the tangent to the graph at the point where x=p is given by

m=b+2cp+3dp2.

For each polynomial,

(a) Find the formula for the slope of the tangent to the graph at the point where x=p.

(b) Find the equation of the tangent to the graph at the point where x=p=-1.

(c) Find each critical point (both the x and y values).

(d) Find f(x) at x=0,2,-2,3,-3,10,-10. Also find the slope m at each of these values.

(e) Use the information found above to sketch the graph.

1. y=x²-2x-3

2. y=4+4x-x²

3. y=2x³+3x²-12x+7

4. y=x³-12x

5. y=x²(4x+3)+1