Question

f(x)=x-x^2 at (-4,-20) .. find an equation for the line tangent to the graph of the function at the indicated point

Answer 1

The slope at that point is the derivative of the function at that point. Take the derivative of f(x) and you get f'(x)= 1 -2x
Plugging in -4 gives you 9, so the slope at that point is 9. Since you want the line tangent that means the slope is the same. So the equation of this line has slope 9 and goes through (-4, -20). Proceed to apply the point-slope formula. You get y+20 = 9(x+4), which simplifies to y = 9x + 16