Calculus of Powers

Package of problems

Original curves

Now that we have discovered which one of each pair of lines is the tangent line and which is the normal, can we recover the original curve that each gradient function (derivative) came from?

1. $2x+5$

2. $15x^2+12x+3$

3. $\dfrac{-2}{x^2}$

4. $24x^2-8x+6$

In each case can you find the equation of the curve which has the given gradient function and the previously matched tangent and normal lines?