Question

How do you find the slope of the tangent line `y=x^3-7x^2+4x+9` at x=1?

Answer 1

`-7`

Explanation:

The slope of the tangent line at a particular point is the gradient of the curve at that point. So we differentiate

`y=x^3-7x^2+4x+9`

`(dy)/(dx)=3x^2-14x+4`

`((dy)/(dx))_(x=1)=3xx1^2-14xx1+4`

`((dy)/(dx))_(x=1)=3-14+4=-7`