Question

What is the slope of y=2x³ +3x²−3x−2 at x=1?

Answer 1

$$y'=(2x^3+3x^2-3x-2)'$$

$$=2(3x^2)+3(2x)-3(1)-0$$

$$=6x^2+6x-3$$

$$y'(1)=6(1)^2+6(1)-3=9$$

The slope of $y=2x^3 +3x^2−3x−2$ at $x=1$ is $9.$